Parabolic Differential Equations and Inequalities with Several Time Variables.
Parabolic equations involving 0th and 1st order terms with L1 data.
This paper is devoted to general parabolic equations involving 0th and 1st order terms, in linear and nonlinear expressions, while the data only belong to L1. Existence and entropic-uniqueness of solutions are proved.
Parabolic initial-boundary value problems in Orlicz spaces
We prove some time mollification properties and imbedding results in inhomogeneous Orlicz-Sobolev spaces which allow us to solve a second order parabolic equation in Orlicz spaces.
Parabolic partial differential equations with memory
Periodic parabolic problems with nonlinearities indefinite in sign.
Let Ω ⊂ RN be a smooth bounded domain. We give sufficient conditions (which are also necessary in many cases) on two nonnegative functions a, b that are possibly discontinuous and unbounded for the existence of nonnegative solutions for semilinear Dirichlet periodic parabolic problems of the form Lu = λa (x, t) up - b (x, t) uq in Ω × R, where 0 < p, q < 1 and λ > 0. In some cases we also show the existence of solutions uλ in the interior of the positive cone and that uλ can...
Periodic solutions in superlinear parabolic problems.
Periodic solutions of partial differential equations with hysteresis
Perona-Malik equation: properties of explicit finite volume scheme
The Perona–Malik nonlinear parabolic problem, which is widely used in image processing, is investigated in this paper from the numerical point of view. An explicit finite volume numerical scheme for this problem is presented and consistency property is proved.
Perturbations and nonlinear harmonic spaces. (Perturbations et espaces harmoniques non linéares.)
Poincaré's inequality and global solutions of a nonlinear parabolic equation
Processus associés à l'équation des milieux poreux