相关论文: Nonlocal porous medium equation: Barenblatt profil…
We study a generalization of the porous medium equation involving nonlocal terms. More precisely, explicit self-similar solutions with compact support generalizing the Barenblatt solutions are constructed. We also present a formal argument…
We study a quite general family of nonlinear evolution equations of diffusive type with nonlocal effects. More precisely, we study porous medium equations with a fractional Laplacian pressure, and the problem is posed on a bounded space…
The nonlocal porous medium equation considered in this paper is a degenerate nonlinear evolution equation involving a space pseudo-differential operator of fractional order. This space-fractional equation admits an explicit, nonnegative,…
The final goal of this paper is to prove existence of local (strong) solutions to a (fully nonlinear) porous medium equation with blow-up term and nondecreasing constraint. To this end, the equation, arising in the context of Damage…
This paper is devoted to the analysis of non-negative solutions for a generalisation of the parabolic equation with porous medium like nonlinear diffusion and nonlinear nonlocal reaction. We investigate under which conditions equilibration…
In this paper, we study the solvability of a Cauchy- Dirichlet problem for nonlinear parabolic equation with non standard growths and nonlocal terms. We show the existence of weak solutions of the considered problem under more general…
We study the Cauchy problem for $p$-adic nonlinear evolutionary pseudo-differential equations for complex-valued functions of a real positive time variable and p-adic spatial variables. Among the equations under consideration there is the…
The long time behaviour of solutions to generalised stochastic porous media equations on bounded domains with Dirichlet boundary data is studied. We focus on a degenerate form of nonlinearity arising in self-organised criticality. Based on…
We consider nonlinear nonlocal diffusive evolution equations, governed by fractional Laplace-type operators, fractional time derivative and involving porous medium type nonlinearities. Existence and uniqueness of weak solutions are…
We consider a possibly degenerate porous media type equation over all of $\R^d$ with $d = 1$, with monotone discontinuous coefficients with linear growth and prove a probabilistic representation of its solution in terms of an associated…
We study a nonlocal evolution equation that involves a pseudo-parabolic third-order term. The equation models almost uni-directional two-phase flow in Brinkman regimes. We prove the existence of weak solutions for this equation. We also…
In this short note we consider a nonlinear and spatially nonlocal PDE modelling moisture evolution in a porous medium. We then show that it naturally arises as a description of superdiffusive jump phenomenon occurring in the medium. We…
This paper studies the derivation of the quadratic porous medium equation and a class of cross-diffusion systems from nonlocal interactions. We prove convergence of solutions of a nonlocal interaction equation, resp. system, to solutions of…
This paper deals with a nonlinear degenerate parabolic equation of order $\alpha$ between 2 and 4 which is a kind of fractional version of the Thin Film Equation. Actually, this one corresponds to the limit value $\alpha=4$ while the Porous…
We study the Cauchy problem for non-linear non-local operators that may be degenerate. Our general framework includes cases where the jump intensity is allowed to depend on the values of the solution itself, e.g. the porous medium equation…
In this paper, we systematically study weak solutions of a linear singular or degenerate parabolic equation in a mixed divergence form and nondivergence form, which arises from the linearized fast diffusion equation and the linearized…
Backward stochastic partial differential equations of parabolic type in bounded domains are studied in the setting where the coercivity condition is not necessary satisfied and the equation can be degenerate. Some generalized solutions…
We consider quasi-static poroelastic systems with incompressible constituents. The nonlinear permeability is taken to be dependent on solid dilation, and physical types of boundary conditions (Dirichlet, Neumann, and mixed) for the fluid…
We consider the Cauchy problem for doubly non-linear degenerate parabolic equations on Riemannian manifolds of infinite volume, or in $\R^N$. The equation contains a weight function as a capacitary coefficient which we assume to decay at…
This article is concerned with a porous medium equation whose pressure law is both nonlinear and nonlocal, namely $\partial_t u = { \nabla \cdot} \left(u \nabla(-\Delta)^{\frac{\alpha}{2}-1}u^{m-1} \right)$ where $u:\mathbb{R}_+\times…