[1] Instantaneous unboundedness of the entropy and uniform positivity of the temperature for the compressible Navier-Stokes equations with fast decay density

[2] On classical solutions to the Cauchy problem of the two-dimensional barotropic compressible Navier-Stokes equations with vacuum

[3] Cutoff Boltzmann equation with polynomial perturbation near Maxwellian

[4] Weyl-type asymptotic formula for Schr\"odinger operators on unbounded fractal spaces

[5] The existence of the solution of the wave equation on graphs

[6] Semilinear heat equations and parabolic variational inequalities on graphs

[7] Calculus of variations on locally finite graphs

[8] A heat flow for the mean field equation on a finite graph

[9] Existence of Solutions to Mean Field Equations on Graphs

[10] Blow-up problems for nonlinear parabolic equations on locally finite graphs

[11] Harnack and mean value inequalities on graphs

[12] Log-Sobolev Inequalities on Graphs with Positive Curvature

[13] On-diagonal lower estimate of heat kernels on graphs

[14] Existence of positive solutions to some nonlinear equations on locally finite graphs

[15] Kazdan-Warner equation on graph

[16] Effective fronts of polygon shapes in two dimensions

[17] Convergence rate for the homogenization of stationary diffusions in dilutely perforated domains with reflecting boundaries

[18] High order homogenized Stokes models capture all three regimes

[19] Layer potentials for Lamé systems and homogenization of perforated elastic medium with clamped holes

[20] Effective Fronts of Polytope Shapes

[21] Generalized ergodic problems: Existence and uniqueness structures of solutions

[22] A Unified Homogenization Approach for the Dirichlet Problem in Perforated Domains

[23] A backscattering model based on corrector theory of homogenization for the random Helmholtz equation

[24] Large time average of reachable sets and Applications to Homogenization of interfaces moving with oscillatory spatio-temporal velocity

[25] Homogenization of randomly deformed conductivity resistant membranes

[26] Localization, Stability, and Resolution of Topological Derivative Based Imaging Functionals in Elasticity

[27] Passive Array Correlation-Based Imaging in a Random Waveguide

[28] Corrector Analysis of a Heterogeneous Multi-scale Scheme for Elliptic Equations with Random Potential

[29] Radiative transfer and diffusion limits for wave field correlations in locally shifted random media

[30] Target Identification Using Dictionary Matching of Generalized Polarization Tensors

[31] Quantitative thermo-acoustic imaging: an exact reconstruction formula

[32] Resolution and stability analysis in acousto-electric imaging

[33] Corrector theory for elliptic equations with long-range correlated random potential

[34] Corrector theory for elliptic equations in random media with singular Green’s function. application to random boundaries

[35] Homogenization and Corrector Theory for Linear Transport in Random Media

[36] Positivity-preserving third order DG schemes for Poisson-Nernst-Planck equations

[37] On time-splitting methods for nonlinear Schrödinger equation with highly oscillatory potential

[38] Two exponential-type integrators for the “good” Boussinesq equation

[39] Regularized numerical methods for the logarithmic Schrödinger equation

[40] Scattering and uniform in time error estimates for splitting method in NLS

[41] Nonuniqueness and nonlinear instability of Gaussons under repulsive harmonic potential

[42] The Kinetic Fokker Planck equation with General Force

[43] Propagation of regularity and long time behavior of the 3D massive relativistic transport equation II: Vlasov-Maxwell system.

[44] Propagation of regularity and long time behavior of 3D massive relativistic transport equation I: Vlasov-Nordström system

[45] Global regularity for the 3D finite depth capillary water waves

[46] Conservation-dissipation formalism of irreversible thermodynamics

[47] A novel construction of thermodynamically compatible models and its correspondence with Boltzmann-equation-based moment-closure hierarchies

[48] PT symmetry in a fractional Schrödinger equation

[49] Zero-viscosity Limit for Boussinesq Equations with Vertical Viscosity and Navier Boundary in the Half Plane

[50] Nonlinear Asymptomatic Stability of Gravitational Hydrostatic Equilibrium for Viscous White Dwarfs with Symmetric Perturbations

[51] Boundary layer and asymptotic stability for the Navier–Stokes–Poisson equations with nonslip boundary conditions

[52] Multi-scale nonlinear singular limit for thermal non-equilibrium gas flow with multiple non-equilibrium modes for analytic data in multi-dimensions with physical boundaries

[53] Generalized hydrodynamics and the classical hydrodynamic limit

[54] Traveling edge states in massive Dirac equations along slowly varying edges

[55] Wave packets in the fractional nonlinear Schrödinger equation with a honeycomb potential

[56] Wave packet dynamics in slowly modulated photonic graphene

[57] Global regularity for the Monge-Ampère equation with natural boundary condition

[58] Resonances over a potential well in an island

[59] Multiplication in Sobolev spaces, revisited

[60] Spectral asymptotics of Laplacians related to one-dimensional graph-directed self-similar measures with overlaps

[61] Radial variation of Bloch functions on the unit ball of ℝ^d

[62] A multiplicity result for a non-local parametric problem with periodic boundary conditions

[63] Stable solutions to semilinear elliptic equations are smooth up to dimension 9

[64] A new hydrostatic reconstruction scheme based on subcell reconstructions

[65] A Mixed Discontinuous Galerkin Method Without Interior Penalty for Time-Dependent Fourth Order Problems

[66] Existence of Multi-dimensional Contact Discontinuities for the Ideal Compressible Magnetohydrodynamics

[67] Propagation of uniform boundedness of entropy and inhomogeneous regularities for viscous and heat conductive gases with far field vacuum in three dimensions

[68] Global strong solutions to the Cauchy problem of the planar non-resistive magnetohydrodynamic equations with large initial data

[69] The primitive equations approximation of the anisotropic horizontally viscous Navier-Stokes equations

[70] Global well-posedness of $z$-weak solutions to the primitive equations without vertical diffusivity

[71] Local existence and uniqueness of heat conductive compressible Navier-Stokes equations in the presence of vacuum and without initial compatibility conditions

[72] Schrodinger equations defined by a class of self-similar measures

[73] Strong damping wave equations defined by a class of self-similar measures with overlaps,

[74] Control of eigenfunctions on surfaces of variable curvature

[75] Fu-Yau Hessian equation

[76] The Mathematics of Shock Reflection-Diffraction and von Neumann's conjectures

[77] The weyl problem in warped product spaces

[78] Estimation of the heat conducted by a cluster of small cavities and characterization of the equivalent heat conduction

[79] Recovering the boundary corrosion from electrical potential distribution using partial boundary data

[80] Zeros of the deformed exponential function

[81] Existence and Multiplicity of Nontrivial Solutions for Biharmonic Equations with Singular Weight Functions

[82] On the Solvability of An Indefinite Nonlinear Kirchhoff Equation via Associated Eigenvalue Problems

[83] Normalized solutions for a coupled Schr\"odinger system

[84] Nonhexagonal lattices from a two species interacting system

[85] On the constant scalar curvature K\"ahler metrics-general automorphism group

[86] On the constant scalar curvature K\"ahler metrics-apriori estimates

[87] Geometric estimates for complex Monge-Ampere equations

[88] On $l_p$-estimates for elliptic and parabolic equations with $a_p$ weights

[89] Global well-posedness of the one-dimensional compressible navier-stokes equations with constant heat conductivity and nonnegative density

[90] Entropy bounded solutions to the one-dimensional compressible Navier-Stokes equations with zero heat conduction and far field vacuum

[91] Entropy-bounded solutions to the one-dimensional heat conductive compressible Navier--Stokes equations with far field vacuum

[92] Global regularity of weak solutions to quasilinear elliptic and parabolic equations with controlled growth

[93] Regularity criteria for the dissipative quasi-geostrophic equations in Hlder spaces

[94] Gradient estimates for parabolic and elliptic systems from linear laminates

[95] Well-posedness for a transport equation with nonlocal velocity

[96] Parabolic and elliptic systems in divergence form with variably partially BMO coefficients

[97] Higher order elliptic and parabolic systems with variably partially BMO coefficients in regular and irregular domains

[98] Dissipative quasi-geostrophic equations in critical Sobolev spaces: smoothing effect and global well-posedness

[99] Global well-posedness and a decay estimate for the critical dissipative quasi-geostrophic equation in the whole space

[100] Stability of Contact Waves for Navier-Stokes Equations and Boltzmann Equation

[101] Time periodic solutions of the Navier-Stokes equations in unbounded cylindrical domains---Leray's problem for periodic flows

[102] A new nonlinear functional for general scalar conservation laws

[103] A characterization of probability measure with finite moment and an application to the Boltzmann equation

[104] Well-posedness of thermal layer equations for inviscid compressible flows

[105] A class of self-similar solutions to a singular and degenerate diffusion equation

[106] A nonlinear functional for general scalar hyperbolic conservation laws

[107] Existence of local solutions for the Boltzmann equation without angular cutoff

[108] Waiting time for a non-Newtonian polytropic filtration equation with convection

[109] Global existence for the ellipsoidal BGK model with initial large oscillations

[110] Well-posedness in Gevrey function space for the three-dimensional Prandtl equations

[111] The Boltzmann equation without angular cutoff. Global existence and full regularity of the Boltzmann equation without angular cutoff. Part I: Maxwellian case and small singularity.

[112] Convergence to the Self-similar Solutions to the Homogeneous Boltzmann Equation

[113] The Boltzmann equation without angular cutoff in the whole space: I, an essential coercivity estimate

[114] Time periodic solution to the compressible Navier-Stokes equations in a periodic domain

[115] Measure valued solutions to the spatially homogeneous Boltzmann equation without angular cutoff

[116] Stability of Nonlinear Wave Patterns to the Bipolar VlasovPoissonBoltzmann System

[117] Compactness Framework ofLpApproximate Solutions for Scalar Conservation Laws

[118] Existence of global smooth solutions for Euler equations with symmetry (II)

[119] Global structure and asymptotic behavior of weak solutions to flood wave equations

[120] The Boltzmann equation with soft potentials near a local Maxwellian

[121] The rate of asymptotic convergence of strong detonations for a model problem

[122] A note on the new Glimm functional for general systems of hyperbolic conservation laws

[123] Uncertainty principle and regularity for Boltzmann type equations

[124] Existence of the discrete travelling waves for a relaxing scheme

[125] An improved convergence rate of Glimm scheme for general systems of hyperbolic conservation laws

[126] MHD boundary layers in Sobolev spaces without monotonicity, II: Convergence theory

[127] The VlasovMaxwellBoltzmann system near Maxwellians in the whole space with very soft potentials

[128] Moment classification of infinite energy solutions to the homogeneous Boltzmann equation

[129] Spectrum analysis and optimal decay rates of the bipolar Vlasov-Poisson-Boltzmann equations

[130] Optimal convergence rates for the compressible Navier-Stokes equations with potential force

[131] NavierStokes equations with degenerate viscosity, vacuum and gravitational force

[132] Regularity of solutions for the Boltzmann equation without angular cutoff

[133] Uniform L_1 boundedness of solutions of hyperbolic conservation laws

[134] Ill-posedness of the Prandtl equations in Sobolev spaces around a shear flow with general decay

[135] Bounded solutions of the Boltzmann equation in the whole space

[136] A new characterization and global regularity of infinite energy solutions to the homogeneous Boltzmann equation

[137] Existence of stationary solutions to the VlasovPoissonBoltzmann system

[138] Global well-posedness of the Boltzmann equation with large amplitude initial data

[139] A combination of energy method and spectral analysis for study of equations of gas motion

[140] MHD Boundary Layers Theory in Sobolev Spaces Without Monotonicity I: WellPosedness Theory

[141] Optimal convergence rates of Landau equation with external forcing in the whole space

[142] A new Glimm functional and convergence rate of Glimm scheme for general systems of hyperbolic conservation laws

[143] Well-posedness in Gevrey space for the Prandtl equations with non-degenerate critical points

[144] Global smooth solutions for a class of quasilinear hyperbolic systems with dissipative terms

[145] Smoothing effect of the homogeneous Boltzmann equation with measure valued initial datum

[146] Existence and stability of planar diffusion waves for 2-D Euler equations with damping

[147] Lp convergence rates of planar waves for multi-dimensional Euler equations with damping

[148] Convergence rate to stationary solutions for Boltzmann equation with external force

[149] A half-space problem for the Boltzmann equation with specular reflection boundary condition

[150] Global existence to Boltzmann equation with external force in infinite vacuum

[151] A well-posedness theory for the Prandtl equations in three space variables

[152] A sharp decay estimate for positive nonlinear waves

[153] A functional integral approach to shock wave solutions of Euler equations with spherical symmetry

[154] Pointwise estimates and Lp convergence rates to diffusion waves for p-system with damping

[155] Long-time behavior of solutions to the bipolar hydrodynamic model of semiconductors with boundary effect

[156] On the ill-posedness of the Prandtl equations in three-dimensional space

[157] L1 and BV-type stability of the Boltzmann equation with external forces

[158] Stability of a relaxation model with a nonconvex flux

[159] Nonlinear stability of boundary layers of the Boltzmann equation, I. The case M< 1

[160] Local existence with physical vacuum boundary condition to Euler equations with damping

[161] Stability of the one-species VlasovPoissonBoltzmann system

[162] The VlasovPoissonBoltzmann system in the whole space: The hard potential case

[163] Stability of contact discontinuity for the Boltzmann equation

[164] Time asymptotic behavior of the bipolar Navier-Stokes-Poisson system

[165] Hypocoercivity of the relativistic Boltzmann and Landau equations in the whole space

[166] One-dimensional Compressible Navier--Stokes Equations with Temperature Dependent Transport Coefficients and Large Data

[167] Weak solutions of general systems of hyperbolic conservation laws

[168] On the convergence rate of vanishing viscosity approximations

[169] The Boltzmann equation without angular cutoff in the whole space: II, Global existence for hard potential

[170] Global solutions to the Boltzmann equation with external forces

[171] Nonlinear stability of rarefaction waves for the Boltzmann equation

[172] Cauchy problem for the VlasovPoissonBoltzmann system

[173] Global existence of classical solutions to the Vlasov-Poisson-Boltzmann system

[174] Optimal decay estimates on the linearized Boltzmann equation with time dependent force and their applications

[175] Regularity of solutions for spatially homogeneous Boltzmann equation without angular cutoff

[176] The Boltzmann equation without angular cutoff in the whole space: Qualitative properties of solutions

[177] Global existence and full regularity of the Boltzmann equation without angular cutoff

[178] The Boltzmann equation without angular cutoff in the whole space: I, Global existence for soft potential

[179] Nonlinear Stability of Strong Rarefaction Waves for Compressible Navier--Stokes Equations

[180] Regularizing effect and local existence for the non-cutoff Boltzmann equation

[181] Compressible Euler equations with vacuum

[182] Contact discontinuity with general perturbations for gas motions

[183] Optimal convergence rates for the compressible NavierStokes equations with potential forces

[184] Compressible NavierStokes equations with degenerate viscosity coefficient and vacuum

[185] Energy method for Boltzmann equation

[186] L1 stability estimates for n n conservation laws

[187] Self-similarity in deterministic and stochastic dissipative systems

[188] Link Flow Correction For Inconsistent Traffic Flow Data Via l1-Minimization

[189] Turbulent Flame Speeds of G-equation Models in Unsteady Cellular Flows

[190] Global solutions and attractors of a Maxwell-Bloch Raman laser system in two transverse dimensions

[191] Scaling limits of waves in convex scalar conservation laws under random initial perturbations

[192] Variational principle based computation of KPP average front speeds in random shear flows

[193] 1-minimization method for link flow correction

[194] A numerical study of fronts in random media using a reactive solute transport model

[195] Computing reactive front speeds in random flows by variational principle

[196] A numerical study of the light bullets interaction in the (2+ 1) sine-Gordon equation

[197] Periodic orbits of the ABC flow with A= B= C= 1

[198] Computing residual diffusivity by adaptive basis learning via spectral method

[199] Existence of traveling waves in a biodegradation model for organic contaminants

[200] Modelling thermal front dynamics in microwave heating

[201] Min-max variational principle and front speeds in random shear flows

[202] Stability, relaxation, and oscillation of biodegradation fronts

[203] Large time asymptotics of solutions to a model combustion system with critical nonlinearity

[204] Comparisons between sine-Gordon and perturbed nonlinear Schrdinger equations for modeling light bullets beyond critical collapse

[205] Periodic homogenization of G-equations and viscosity effects

[206] Sharp asymptotic growth laws of turbulent flame speeds in cellular flows by inviscid HamiltonJacobi models

[207] Asymptotics for turbulent flame speeds of the viscous G-equation enhanced by cellular and shear flows

[208] Front speed in the Burgers equation with a random flux

[209] Bounds on front speeds for inviscid and viscous G-equations

[210] White noise perturbation of the viscous shock fronts of the Burgers equation

[211] Stochastic analysis of biodegradation fronts in one-dimensional heterogeneous porous media

[212] Dynamic stability of vortex solutions of Ginzburg-Landau and nonlinear Schrdinger equations

[213] Existence of multidimensional traveling waves in the transport of reactive solutes through periodic porous media

[214] A variational principle for KPP front speeds in temporally random shear flows

[215] Global solutions to a reactive Boussinesq system with front data on an infinite domain

[216] On the dynamical law of the GinzburgLandau vortices on the plane

[217] Quenching and propagation of bistable reaction-diffusion fronts in multidimensional periodic media

[218] Diffusion-generated motion by mean curvature for filaments

[219] Periodic homogenization of the inviscid G-equation for incompressible flows

[220] Asymptotic spreading of KPP reactive fronts in incompressible space-time random flows

[221] Global large time self-similarity of a thermal-diffusive combustion system with critical nonlinearity

[222] Modeling light bullets with the two-dimensional sineGordon equation

[223] Existence of KPP type fronts in space-time periodic shear flows and a study of minimal speeds based on variational principle

[224] On the incompressible fluid limit and the vortex motion law of the nonlinear Schrdinger equation

[225] Existence and nonexistence of traveling waves and reaction-diffusion front propagation in periodic media

[226] Front propagation in heterogeneous media

[227] Analytical solutions to the 3-D compressible Navier-Stokes equations with free boundaries

[228] Stability of the Superposition of a Viscous Contact Wave with Two Rarefaction Waves to the Bipolar Vlasov--Poisson--Boltzmann System

[229] Global stability of wave patterns for compressible Navier-Stokes system with free boundary

[230] Justification of diffusion limit for the Boltzmann equation with a non-trivial profile

[231] L2-contraction of large planar shock waves for multi-dimensional scalar viscous conservation laws

[232] Vanishing viscosity of isentropic Navier-Stokes equations for interacting shocks

[233] The Inviscid Limit to a Contact Discontinuity for the Compressible Navier--Stokes--Fourier System Using the Relative Entropy Method

[234] Zero dissipation limit to rarefaction wave with vacuum for one-dimensional compressible NavierStokes equations

[235] Zero dissipation limit of the compressible heat-conducting Navier-Stokes equations in the presence of the shock

[236] Global existence of weak solution to the heat and moisture transport system in fibrous porous media

[237] Large-time behavior of solutions to the inflow problem of full compressible NavierStokes equations

[238] A global unique solvability of entropic weak solution to the one-dimensional pressureless Euler system with a flocking dissipation

[239] Vanishing viscosity limit of the compressible NavierStokes equations for solutions to a Riemann problem

[240] Hydrodynamic limit of the Boltzmann equation with contact discontinuities

[241] Stability of wave patterns to the inflow problem of full compressible NavierStokes equations

[242] Fluid dynamic limit to the Riemann solutions of Euler equations: I. Superposition of rarefaction waves and contact discontinuity

[243] Stability of rarefaction waves to the 1D compressible NavierStokes equations with density-dependent viscosity

[244] Global well-posedness of 2D compressible NavierStokes equations with large data and vacuum

[245] Existence of multiple positive solutions for nonhomogeneous elliptic problems in RN

[246] Multiple positive solutions for a Dirichlet problem involving critical Sobolev exponent

[247] Nonlinear Differential Equations in Geometry and Physics.

[248] Real time solution of Duncan-Mortensen-Zakai equation without memory

[249] Existence and uniqueness of solutions for Duncan-Mortensen-Zakai equations

[250] Segmentation and tracking of 3D neuron microscopy images using a PDE based method and connected component labeling algorithm

[251] Finite-dimensional filters with nonlinear drift. V: solution to Kolmogorov equation arising from linear filtering with non-Gaussian initial condition

[252] Existence and decay estimates for time dependent parabolic equation with application to DuncanMortensenZakai equation