Related papers: Existence of Strong Solutions for Stochastic Porou…
We prove existence and uniqueness of solutions to a class of porous media equations driven by the fractional Laplacian when the initial data are positive finite Radon measures on the Euclidean space. For given solutions without a prescribed…
We construct examples of solutions to the incompressible porous media (IPM) equation that must exhibit infinite in time growth of derivatives provided they remain smooth. As an application, this allows us to obtain nonlinear instability for…
In this paper, we study the existence and uniqueness of weak solution of a nonlinear poroelasticity model. To better describe the proccess of deformation and diffusion underlying in the original model, we firstly reformulate the nonlinear…
We consider possibly degenerate and singular elliptic equations in a possibly anisotropic medium. We obtain monotonicity results for the energy density, rigidity results for the solutions and classification results for the…
We prove global well-posedness in the strong sense for stochastic generalized porous media equations driven by square integrable martingales with stationary independent increments.
In this paper, we establish smoothness of moments of the solutions of discrete coagulation-diffusion systems. As key assumptions, we suppose that the coagulation coefficients grow at most sub-linearly and that the diffusion coefficients…
A stochastic differential equation with infinite memory is considered. The drift coefficient of the equation is a nonlinear functional of the past history of the solution. Sufficient conditions for existence and uniqueness of stationary…
The existence of martingale solutions for stochastic porous media equations driven by nonlinear multiplicative space-time white noise is established in spatial dimension one. The Stroock-Varopoulos inequality is identified as a key tool in…
We consider the mixed formulation of the equations governing Darcy-Forchheimer flow in porous media. We prove existence and uniqueness of a solution for the stationary problem and the existence of a solution for the transient problem.
We prove the pathwise well-posedness of stochastic porous media and fast diffusion equations driven by nonlinear, conservative noise. As a consequence, the generation of a random dynamical system is obtained. This extends results of the…
In this work, we investigate a model describing flow through porous media with permeability heterogeneity, combining an advection-reaction-diffusion equation for solute concentration with an unsteady Darcy-Brinkman equation with Korteweg…
We establish the existence of smooth, finite-energy solutions to the 2D incompressible porous media equation (IPM), with a compactly supported uniformly smooth source, which develop singularities in finite time.
We are concerned with the existence and uniqueness of solutions with only bounded density for the barotropic compressible Navier-Stokes equations. Assuming that the initial velocity has slightly sub-critical regularity and that the initial…
We obtain sufficient conditions for the uniqueness of solutions to the Cauchy problem for the continuity equation in classes of measures that need not be absolutely continuous.
We analyze long-time behavior of solutions to a class of problems related to very fast and singular diffusion porous medium equations having nonhomogeneous in space and time source terms with zero mean. In dimensions two and three, we…
We study existence and uniqueness of bounded solutions to a fractional nonlinear porous medium equation with a variable density, in one space dimension.
We prove the existence of strong solutions of It\^o's stochastic time dependent equations with irregular diffusion and drift terms of Morrey spaces. Strong uniqueness is also discussed.
We present a generalization of Krylov-Rozovskii's result on the existence and uniqueness of solutions to monotone stochastic differential equations. As an application, the stochastic generalized porous media and fast diffusion equations are…
The Monotonicity inequality is an important tool in the understanding of existence and uniqueness of strong solutions for Stochastic PDEs. In this article, we discuss three approaches to establish this deterministic inequality explicitly.
We prove a well-posedness result for stochastic Allen-Cahn type equations in a bounded domain coupled with generic boundary conditions. The (nonlinear) flux at the boundary aims at describing the interactions with the hard walls and is…