Radial symmetric solutions of the Cahn-Hilliard equation with degenerate mobility.
Rate of convergence of finite-difference approximations for degenerate linear parabolic equations with and coefficients.
Reaction-diffusion in nonsmooth and closed domains.
Regularity for entropy solutions of parabolic p-Laplacian type equations.
In this note we give some summability results for entropy solutions of the nonlinear parabolic equation ut - div ap (x, ∇u) = f in ] 0,T [xΩ with initial datum in L1(Ω) and assuming Dirichlet's boundary condition, where ap(.,.) is a Carathéodory function satisfying the classical Leray-Lions hypotheses, f ∈ L1 (]0,T[xΩ) and Ω is a domain in RN. We find spaces of type Lr(0,T;Mq(Ω)) containing the entropy solution and its gradient. We also include some summability results when f = 0 and the p-Laplacian...
Regularity of solutions of nonlinear degenerate parabolic systems.
Regularity of solutions of the fractional porous medium flow
We study a porous medium equation with nonlocal diffusion effects given by an inverse fractional Laplacian operator. The precise model is . The problem is posed in with nonnegative initial data that are integrable and decay at infinity. A previous paper has established the existence of mass-preserving, nonnegative weak solutions satisfying energy estimates and finite propagation. As main results we establish the boundedness and regularity of such weak solutions. Finally, we extend the existence...
Regularity of solutions to doubly nonlinear diffusion equations.
Regularity of the interface for the porous medium equation.
Relaxation approximations and bounded variation estimates for some partial differential equations.
Remarks on quenching.
Renormalized entropy solutions for degenerate nonlinear evolution problems.
Renormalized solution for nonlinear degenerate problems in the whole space
We consider the general degenerate parabolic equation :We suppose that the flux is continuous, is nondecreasing continuous and both functions are not necessarily Lipschitz. We prove the existence of the renormalized solution of the associated Cauchy problem for initial data and source term. We establish the uniqueness of this type of solution under a structure condition and an assumption on the modulus of continuity of . The novelty of this work is that , , , , are not Lipschitz...
Renormalized solutions of a nonlinear parabolic equation with double degeneracy.
Reverse smoothing effects, fine asymptotics, and Harnack inequalities for fast diffusion equations.
Rothe's method for degenerate quasilinear parabolic equations