Regularity of solutions of nonlinear degenerate parabolic systems.
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...
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...
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.