The fast diffusion equation with measure data

The Porous Medium Equation with Measure Data

We study the existence of solutions to the porous medium equation with a nonnegative, finite Radon measure on the right hand side. We show that such problems have solutions in a wide class of supersolutions. These supersolutions are defined as lower semicontinuous functions obeying a parabolic comparison principle with respect to continuous solutions. We also consider the question of how the in...

TRANSPORT EQUATION WITH FUZZY DATA

In this paper, we use the generalized differentiability concept tostudy the fuzzy transport equation. We consider transport equationin the homogeneous and non-homogeneous cases with fuzzy initialcondition. We also present the solution when speed parameter is a fuzzynumber. Our method is based on the construction of the solutionsby employing Zadeh's extension principle.

Extended solutions for general Fast Diffusion Equations with optimal measure data

We study the theory of existence and uniqueness of nonlinear diffusion equations of the form ut = ∆φ(u) in R × (0,∞), where φ : R+ → R+ is a continuous and increasing function. We focus on the fast diffusion type by imposing the growth condition : m1 6 sφ′(s) φ(s) 6 m2, for some constants 0 < m1 6 m2 < 1 and all s > 0. Moreover, m1 > (N − 2)/N . Existence is obtained for an optimal class of ini...

Numerical solution of a fast diffusion equation

In this paper, the authors consider the first boundary value problem for the nonlinear reaction diffusion equation: ut −∆um = αup1 in Ω, a smooth bounded domain in Rd(d ≥ 1) with the zero lateral boundary condition and with a positive initial condition, m ∈ ]0, 1[ (fast diffusion problem), α ≥ 0 and p1 ≥ m. Sufficient conditions on the initial data are obtained for the solution to vanish or bec...

Fast Diffusion Equation with Critical Sobolev Exponent in a Ball