相关论文: Quasilinear generalized parabolic Anderson model e…
We consider a parabolic sine-Gordon model with periodic boundary conditions. We prove a fundamental maximum principle which gives a priori uniform control of the solution. In the one-dimensional case we classify all bounded steady states…
Numerical investigations of partial differential equations with hysteresis have largely focused on simulations, leaving numerical error analysis unexplored and relying mainly on derivative-free nonlinear solvers. This work establishes…
We announce some new results for proving H\"older continuity of weak solutions to quasilinear parabolic equations whose prototype takes the form $$u_t - div (|\nabla u|^{p-2}\nabla u)= 0 \qquad \text{or} \qquad u_t - div…
We consider the parabolic Anderson model (PAM) which is given by the equation $\partial u/\partial t = \kappa\Delta u + \xi u$ with $u\colon\, \Z^d\times [0,\infty)\to \R$, where $\kappa \in [0,\infty)$ is the diffusion constant, $\Delta$…
We study a higher order parabolic partial differential equation that arises in the context of condensed matter physics. It is a fourth order semilinear equation whose nonlinearity is the determinant of the Hessian matrix of the solution. We…
In this work we study a dissipative one dimensional scalar parabolic problem with non-local nonlinear diffusion with delay. We consider the general situation in which the functions involved are only continuous and solutions may not be…
We study local and global existence of solutions for some semilinear parabolic initial boundary value problems with autonomous nonlinearities having a "Newtonian" nonlocal term.
We are interested in (uniformly) parabolic PDEs with a nonlinear dependance of the leading-order coefficients, driven by a rough right hand side. For simplicity, we consider a space-time periodic setting with a single spatial variable:…
We study the Dirichlet problem for the semi--linear partial differential equations ${\rm div}\,(A\nabla u)=f(u)$ in simply connected domains $D$ of the complex plane $\mathbb C$ with continuous boundary data. We prove the existence of the…
We prove a local higher integrability result for the spatial gradient of weak solutions to doubly nonlinear parabolic systems whose prototype is $$ \partial_t \left(|u|^{q-1}u \right) -\operatorname{div} \left( |Du|^{p-2} Du \right) =…
We examine the stability of a class of quasilinear parabolic partial differential equations under perturbations. We are interested in the behavior of viscosity solutions as the perturbation parameter vanishes and establish explicit…
In this paper we study the quasilinear nondiagonal parabolic type systems. We assume that the principal elliptic operator, which is part of the parabolic system, has a divergence structure. Under certain conditions it is proved the…
We establish Schauder-type estimates for linear parabolic systems driven by variable-coefficient nonlocal pseudo-differential operators of order $s>0$. These estimates are formulated in critical time-weighted H\"older/Besov-type spaces and…
A probabilistic representation for initial value semilinear parabolic problems based on generalized random trees has been derived. Two different strategies have been proposed, both requiring generating suitable random trees combined with a…
Time fractional parabolic problem for p-Laplacian with double singular Hardy-type potential is considered. Comparison principle and appriory estimates for the weak solutions are proved. Existence of global weak solutions and finite-time…
In this paper, we establish the existence of a solution for a class of quasilinear equations characterized by the prototype: \begin{equation} \left\{\begin{aligned} -\operatorname{div}(\vartheta_\alpha|\nabla u|^{p-2} \nabla…
In this paper we obtain necessary conditions and sufficient conditions on the initial data for the solvability of the Cauchy problem $$ \partial_t u+(-\Delta)^{\frac{\theta}{2}}u=u^p,\quad x\in{\bf R}^N,\,\,t>0, \qquad u(0)=\mu\ge…
We investigate a class of elliptic and parabolic partial differential equations driven by p(u) laplacian. This dependence necessitates the use of variable exponent Sobolev spaces specifically tailored to the anisotropic framework. For the…
We study local regularity for nonlocal doubly degenerate parabolic equations. The model equation is \begin{equation*}\begin{split}…
We prove the global existence of small data solution in all space dimension for weakly coupled systems of semi-linear effectively damped wave, with different time-dependent coefficients in the dissipation terms. Moreover, nonlinearity terms…