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
Schauder estimates for a class of degenerate elliptic and parabolic operators with unbounded coefficients in
Self-similar singular solution of doubly singular parabolic equation with gradient absorption term.
Self-similar solutions for a nonlinear degenerate parabolic equation.
Self-similar solutions of convection-diffusion processes.
Semidifferentials, quadratic forms and fully nonlinear elliptic equations of second order
Sets of admissible initial data for porous-medium equations with absorption.
Singular Perturbations for a Class of Degenerate Parabolic Equations with Mixed Dirichlet-Neumann Boundary Conditions
We establish a singular perturbation property for a class of quasilinear parabolic degenerate equations associated with a mixed Dirichlet-Neumann boundary condition in a bounded domain of , . In order to prove the -convergence of viscous solutions toward the entropy solution of the corresponding first-order hyperbolic problem, we refer to some properties of bounded sequences in together with a weak formulation of boundary conditions for scalar conservation laws.
Singular solutions of doubly singular parabolic equations with absorption.
Smoothing properties in multistep backward difference method and time derivative approximation for linear parabolic equations.