The pressure equation in the fast diffusion range.
The relation between the porous medium and the eikonal equations in several space dimensions.
We study the relation between the porous medium equation ut = Δ(um), m > 1, and the eikonal equation vt = |Dv|2. Under quite general assumtions, we prove that the pressure and the interface of the solution of the Cauchy problem for the porous medium equation converge as m↓1 to the viscosity solution and the interface of the Cauchy problem for the eikonal equation. We also address the same questions for the case of the Dirichlet boundary value problem.
The support shrinking properties for solutions of quasilinear parabolic equations with strong absorption terms
The Wolff gradient bound for degenerate parabolic equations
The spatial gradient of solutions to non-homogeneous and degenerate parabolic equations of -Laplacean type can be pointwise estimated by natural Wolff potentials of the right hand side measure.
Theoretical analysis of a model of the thermal boundary layer with drag.
Time-discretization of a degenerate reaction-diffusion equation arising in biofilm modeling.
Travelling wave for absorption-convection-diffusion equations.
Two Numerical Methods for the elliptic Monge-Ampère equation
The numerical solution of the elliptic Monge-Ampère Partial Differential Equation has been a subject of increasing interest recently [Glowinski, in 6th International Congress on Industrial and Applied Mathematics, ICIAM 07, Invited Lectures (2009) 155–192; Oliker and Prussner, Numer. Math.54 (1988) 271–293; Oberman, Discrete Contin. Dyn. Syst. Ser. B10 (2008) 221–238; Dean and Glowinski, in Partial differential equations, Comput. Methods Appl. Sci. 16 (2008) 43–63; Glowinski et al., Japan...
Type II collapsing of maximal solutions to the Ricci flow in
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.