Solvability of boundary value problems for strongly degenerate parabolic equations with discontinuous coefficients
Hiroshi Watanabe · Discrete and Continuous Dynamical Systems - S · 2013
In this paper we consider the initial boundary value problem for strongly degenerate parabolic equations with discontinuous coefficients. This equation has the both properties of parabolic equation and hyperbolic equation. Moreover, approximate solutions for this equation may not belong to $BV$. These are difficult points for this type of equations. We consider the type of equations under the zero-flux boundary conditions. In particular, we prove the existence and partial uniqueness of weak solutions to such problems. Our proof use the compactness theorem derived by Panov [14] and the estimate of degenerate diffusion term derived by Karlsen-Risebro-Towers [10].