Related papers: Local and global time decay for parabolic equation…
In this paper, we study the backward problem of determining initial condition for some class of nonlinear parabolic equations in multidimensional domain where data are given under random noise. This problem is ill-posed, i.e., the solution…
The parareal in time algorithm allows to perform parallel simulations of time dependent problems. This algorithm has been implemented on many types of time dependent problems with some success. Recent contributions have allowed to extend…
We study a mathematical model describing the dynamics of dislocation densities in crystals. This model is expressed as a one-dimensional system of a parabolic equation and a first order Hamilton-Jacobi equation that are coupled together. We…
This paper is concerned with geometric motion of a closed surface whose velocity depends on a nonlocal quantity of the enclosed region. Using the level set formulation, we study a class of nonlocal Hamilton--Jacobi equations and establish a…
In this paper, we study the global regularity and sharp decay rates for the isentropic hypo-viscous compressible Navier-Stokes equations in 1D. Firstly, we prove the global stability for the small initial data near a stable equilibrium.…
In this paper, we study the large time behavior of solutions of a class of parabolic fully nonlinear integro-differential equations in a periodic setting. In order to do so, we first solve the ergodic problem}(or cell problem), i.e. we…
We study the Hamilton-Jacobi equation for undiscounted exit time control problems with general nonnegative Lagrangians using the dynamic programming approach. We prove theorems characterizing the value function as the unique…
Subdiffusive motion takes place at a much slower timescale than diffusive motion. As a preliminary step to studying reaction-subdiffusion pulled fronts, we consider here the hyperbolic limit $(t,x) \to (t/\varepsilon, x/\varepsilon)$ of an…
In this paper, we mainly study the global strong solutions and its long time decay rates of all order spatial derivatives to a micro-macro model for compressible polymeric fluids with small initial data. This model is a coupling of…
We obtain new a priori estimates for the nonnegative solutions of the equation \[ u_{t}-\Delta u+|\nabla u|^{q}=0 \] in $Q_{\Omega,T}=\Omega\times\left( 0,T\right) ,$ $T\leqq\infty,$ where $q>0,$ and $\Omega=\mathbb{R}^{N},$ or $\Omega$ is…
We consider a parabolic partial differential equation with Dirichlet boundary conditions and measure or $L^1$ data. The key difficulty consists in a presence of a monotone operator~$A$ subjected to a non-standard growth condition,…
In this paper, we consider the finite time blow-up results for a parabolic equation coupled with superlinear source term and local linear boundary dissipation. Using a concavity argument, we derive the sufficient conditions for the…
Consider the Cauchy problem of incompressible Navier-Stokes equations in $\mathbb{R}^3$ with uniformly locally square integrable initial data. If the square integral of the initial datum on a ball vanishes as the ball goes to infinity, the…
We establish temporal decay estimates for weak solutions to the Hall-magnetohydrodynamic equations. With these estimates in hand we obtain algebraic time decay for higher order Sobolev norms of small initial data solutions.
In this paper we show a uniqueness result for weak epigraphical solutions of Hamilton-Jacobi-Bellman (HJB) equations on infinite horizon for a class of lower semicontinuous functions vanishing at infinity. Weak epigraphical solutions of HJB…
We consider the Cauchy problem for the spatially inhomogeneous Landau equation with soft potentials in the case of large (i.e. non-perturbative) initial data. We construct a solution for any bounded, measurable initial data with uniform…
We argue that Hamilton-Jacobi equations provide a convenient and intuitive approach for studying the large-scale behavior of mean-field disordered systems. This point of view is illustrated on the problem of inference of a rank-one matrix.…
We study the homogenization of nonlinear, first-order equations with highly oscillatory mixing spatio-temporal dependence. It is shown in a variety of settings that the homogenized equations are stochastic Hamilton-Jacobi equations with…
We give a new representation formula for solutions to nonconvex first-order Hamilton--Jacobi equations in the periodic setting and present some applications. We then prove the large time behavior for solutions under some additional…
In this article we develop an analogue of Aubry Mather theory for time periodic dissipative equation \[ \left\{ \begin{aligned} \dot x&=\partial_p H(x,p,t),\\ \dot p&=-\partial_x H(x,p,t)-f(t)p \end{aligned} \right. \] with $(x,p,t)\in…