Well-posedness for non-isotropic degenerate parabolic-hyperbolic equations

Well-posedness for Non-isotropic Degenerate Parabolic-hyperbolic Equations

We develop a well-posedness theory for solutions in L to the Cauchy problem of general degenerate parabolic-hyperbolic equations with non-isotropic nonlinearity. A new notion of entropy and kinetic solutions and a corresponding kinetic formulation are developed which extends the hyperbolic case. The notion of kinetic solutions applies to more general situations than that of entropy solutions; a...

Well-posedness and Regularity for Quasilinear Degenerate Parabolic-hyperbolic Spde

We study quasilinear degenerate parabolic-hyperbolic stochastic partial differential equations with general multiplicative noise within the framework of kinetic solutions. Our results are twofold: First, we establish new regularity results based on averaging techniques. Second, we prove the existence and uniqueness of solutions in a full L1 setting requiring no growth assumptions on the nonline...

Well-posedness Results for Triply Nonlinear Degenerate Parabolic Equations

We study the well-posedness of triply nonlinear degenerate ellipticparabolic-hyperbolic problem b(u)t − div ã(u, ∇φ(u)) + ψ(u) = f, u|t=0 = u0 in a bounded domain with homogeneous Dirichlet boundary conditions. The nonlinearities b, φ and ψ are supposed to be continuous non-decreasing, and the nonlinearity ã falls within the Leray-Lions framework. Some restrictions are imposed on the dependence...

WELL- POSEDNESS OF THE ROTHE DIFFERENCE SCHEME FOR REVERSE PARABOLIC EQUATIONS

Well-posedness for Hyperbolic Problems