相关论文: Optimal Weighted Smoothing and Asymptotics of Anci…

We study the global existence of solutions to a one-dimensional drift-diffusion equation with logistic term, generalizing the classical parabolic-elliptic Keller-Segel aggregation equation arising in mathematical biology. In particular, we…

The paper describes a new approach to global smoothing problems for dispersive and non-dispersive evolution equations based on the global canonical transforms and the underlying global microlocal analysis. For this purpose, the Egorov-type…

For the physical vacuum free boundary problem with the sound speed being $C^{{1}/{2}}$-H$\ddot{\rm o}$lder continuous near vacuum boundaries of the three-dimensional compressible Euler equations with damping, the global existence of…

We present a novel approach for the numerical solution of problems of elastic scattering by open arcs in two dimensions. Our methodology relies on the composition of weighted versions of the classical operators associated with Dirichlet and…

We prove an asymptotic formula for the Fourier transform of the arithmetic surface measure associated to the Waring--Goldbach problem and provide several applications, including bounds for discrete spherical maximal functions along the…

We consider the initial-value problem for the ``good'' Boussinesq equation on the line. Using inverse scattering techniques, the solution can be expressed in terms of the solution of a $3 \times 3$-matrix Riemann-Hilbert problem. We…

In this paper, we introduce and analyze a numerical scheme for solving the Cauchy-Dirichlet problem associated with fractional nonlinear diffusion equations. These equations generalize the porous medium equation and the fast diffusion…

This article studies a dirichlet boundary value problem for singularly perturbed time delay convection diffusion equation with degenerate coefficient. A priori explicit bounds are established on the solution and its derivatives. For…

We consider gradient estimates to positive solutions of porous medium equations and fast diffusion equations: $$u_t=\Delta_\phi(u^p)$$ associated with the Witten Laplacian on Riemannian manifolds. Under the assumption that the…

Let $n\ge2$ and $\Omega\subset\mathbb{R}^n$ be a bounded NTA domain. In this article, the authors investigate (weighted) global gradient estimates for Dirichlet boundary value problems of second order elliptic equations of divergence form…

In this paper we prove the existence of smooth solutions to fully nonlinear and nonlocal parabolic equations with critical index. The proof relies on the apriori H\"older estimate for advection fractional-diffusion equation established by…

We prove local smoothing estimates for the Dirac equation on some non-flat manifolds; in particular, we will consider asymptotically flat and warped products metrics. The strategy of the proofs relies on the multiplier method.

In this work, we derive sharp non-asymptotic deviation bounds for weighted sums of Dirichlet random variables. These bounds are based on a novel integral representation of the density of a weighted Dirichlet sum. This representation allows…

We consider the system of partial differential equations governing two-dimensional flows of a robust class of viscoelastic rate-type fluids with stress diffusion, involving a general objective derivative. The studied system generalizes the…

We study a nonlinear porous medium type equation involving the infinity Laplacian operator. We first consider the problem posed on a bounded domain and prove existence of maximal nonnegative viscosity solutions. Uniqueness is obtained for…

In this work, we consider the numerical solution of an initial boundary value problem for the distributed order time fractional diffusion equation. The model arises in the mathematical modeling of ultra-slow diffusion processes observed in…

This paper is concerned with the asymptotic behavior of the solution to the Euler equations with time-depending damping on quadrant $(x,t)\in \mathbb{R}^+\times\mathbb{R}^+$, \begin{equation}\notag \partial_t v - \partial_x u=0, \qquad…

In this paper we propose new insights and ideas to set up quantitative boundary estimates for solutions to Dirichlet problem of a class of fully non-linear elliptic equations on compact Hermitian manifolds with real analytic Levi flat…

In this article a simplified weak Galerkin finite element method is developed for the Dirichlet boundary value problem of convection-diffusion-reaction equations. The simplified weak Galerkin method utilizes only the degrees of freedom on…

We study the elastic time-harmonic wave scattering problems on unbounded domains with boundaries composed of finite collections of disjoints finite open arcs (or cracks) in two dimensions. Specifically, we present a fast spectral Galerkin…