Un problème mixte non-linéaire parabolique provenant de la génétique des populations
Un résultat d'existence de solution faible d'un système parabolique-elliptique non linéaire doublement dégénéré
Uniform attractors for nonautonomous parabolic equations involving weighted p-Laplacian operators
We consider the first initial boundary value problem for nonautonomous quasilinear degenerate parabolic equations involving weighted p-Laplacian operators, in which the nonlinearity satisfies the polynomial condition of arbitrary order and the external force is normal. Using the asymptotic a priori estimate method, we prove the existence of uniform attractors for this problem. The results, in particular, improve some recent ones for nonautonomous p-Laplacian equations.
Uniqueness and existence of solution in the BVt(Q) space to a doubly nonlinear parabolic problem.
In this paper we present some results on the uniqueness and existence of a class of weak solutions (the so called BV solutions) of the Cauchy-Dirichlet problem associated to the doubly nonlinear diffusion equationb(u)t - div (|∇u - k(b(u))e|p-2 (∇u - k(b(u))e)) + g(x,u) = f(t,x).This problem arises in the study of some turbulent regimes: flows of incompressible turbulent fluids through porous media, gases flowing in pipelines, etc. The solvability of this problem is established in the BVt(Q) space....
Uniqueness and stability of regional blow-up in a porous-medium equation
Uniqueness of entropy solutions of nonlinear elliptic-parabolic-hyperbolic problems in one dimension space.
Uniqueness of entropy solutions to nonlinear elliptic-parabolic problems.
Uniqueness of solutions to a class of strongly degenerate parabolic equation.
Uniqueness of solutions to a system of differential inclusions.
Uniqueness of the solution of the Cauchy problem to some equations of nonstationary filtration
Uniqueness of very singular self-similar solution of a quasilinear degenerate parabolic equation with absorption.
We show the uniqueness of the very singular self-similar solution of the equationut - Δ pum + uq = 0.The result is carried out by studying the stationary associate equation and by introducing a suitable change of unknown. That allows to assume the zero-order perturbation term in the new equation to be monotone increasing. A careful study of the behaviour of solutions near the boundary of their support is also used in order to prove the main result.