Related papers: Large time stabilization of rough-data solutions i…

In this paper we study the long-time stability of the Cauchy one-leg theta-methods for the two-dimensional NavierStokes equations. We establish the uniform dissipativity in H^1, in the sense that the semi-discrete-in-time approximations…

Many compactifications of higher-dimensional supersymmetric theories have approximate vacuum degeneracy. The associated moduli fields are stabilized by non-perturbative effects which break supersymmetry. We show that at finite temperature…

In this paper, a backward Euler method combined with finite element discretization in spatial direction is discussed for the equations of motion arising in the $2D$ Oldroyd model of viscoelastic fluids of order one with the forcing term…

Let $\Omega\subset\mathbb{R}^{N}$, $N\geq2$ be a bounded smooth domain and $\alpha>1$. We are interested in the singular elliptic equation% \[ \triangle h=\frac{1}{\alpha}h^{-\alpha}-p\quad\text{in}\Omega \] with Neumann boundary…

Continuous data assimilation addresses time-dependent problems with unknown initial conditions by incorporating observations of the solution into a nudging term. For the prototypical heat equation with variable conductivity and the Neumann…

This paper contributes to the study of large data problems for $C^1$ solutions of the relativistic Euler equations. In the $(1+1)$-dimensional spacetime setting, if the initial data are away from vacuum, a key difficulty in proving the…

We consider the exclusion process in the one-dimensional discrete torus with $N$ points, where all the bonds have conductance one, except a finite number of slow bonds, with conductance $N^{-\beta}$, with $\beta\in[0,\infty)$. We prove that…

\begin{abstract} Motivated by a classical stabilization result for solution to the Cauchy problem of the heat equation$\ \partial_{t}u=\bigtriangleup u\ $on $\mathbb{R}^{n}$, we consider its oscillation behavior with radial initial data…

We consider solutions satisfying the zero Neumann boundary condition and a linearized mean field game equation in $\Omega \times (0,T)$ whose principal coefficients depend on the time and spatial variables with general Hamiltonian, where…

This work considers a model for oncolytic virotherapy, as given by the reaction-diffusion-taxis system $$ \left\{ \begin{array}{l} u_t = \Delta u - \nabla \cdot (u\nabla v)-\rho uz, \\[1mm] v_t = - (u+w)v, \\[1mm] w_t = D_w \Delta w - w +…

In this paper, we consider the fractional heat equation $u_{t}=\triangle^{\alpha/2}u+f(u)$ with Dirichlet boundary conditions on the ball $B_{R}\subset \mathbb{R}^{d}$, where $\triangle^{\alpha/2}$ is the fractional Laplacian,…

We consider the Cauchy problem for a strictly hyperbolic, $n\times n$ system in one space dimension: $u_t+A(u)u_x=0$, assuming that the initial data has small total variation. We show that the solutions of the viscous approximations…

We establish the existence of Lipschitz continuous solutions to the Cauchy Dirichlet problem for a class of evolutionary partial differential equations of the form $$ \partial_tu-\text{div}_x \nabla_\xi f(\nabla u)=0 $$ in a space-time…

We establish the strong comparison principle and strict positivity of solutions to the following nonlinear stochastic heat equation on $\mathbb{R}^d$ \[ \left(\frac{\partial }{\partial t} -\frac{1}{2}\Delta \right) u(t,x) = \rho(u(t,x))…

We consider the fourth order problem $\Delta^{2}u=\lambda f(u)$ on a general bounded domain $\Omega$ in $R^{n}$ with the Navier boundary condition $u=\Delta u=0$ on $\partial \Omega$. Here, $\lambda$ is a positive parameter and $…

We address nonautonomous initial boundary value problems for decoupled linear first-order one-dimensional hyperbolic systems, investigating the phenomenon of finite time stabilization. We establish sufficient and necessary conditions…

Let $\Omega$ be a bounded domain of $\mathbb{R}^{N}$, and $Q=\Omega \times(0,T).$ We first study the problem \[ \left\{ \begin{array} [c]{l}% {u_{t}}-{\Delta_{p}}u=\mu\qquad\text{in }Q,\\ {u}=0\qquad\text{on }\partial\Omega\times(0,T),\\…

This paper presents original and close to optimal stability conditions linking the time step and the space step, stronger than the CFL criterion: $\delta t\leq C\delta x^\alpha$ with $\alpha=\frac{2r}{2r-1}$, $r$ an integer, for some…

We consider periodic homogenization with localized defects of boundary value problems for semilinear ODE systems of the type $$ \Big((A(x/\varepsilon)+B(x/\varepsilon))u'(x)+c(x,u(x))\Big)'= d(x,u(x)) \mbox{ for } x \in (0,1),\;…

We study the limit, when $k\to\infty$ of solutions of $u_t-\Delta u+f(u)=0$ in $R^N\times(0,\infty)$ with initial data $k\gd$, when $f$ is a positive increasing function. We prove that there exist essentially three types of possible…