Existence and Smoothing for a Nondivergence-Form Degenerate Diffusion from Plasma-Wave Theory

William Porteous, Irene M. Gamba, Kun Huang

We prove existence and positive-time smoothing of weak solutions to the degenerate parabolic Cauchy--Dirichlet problem ${\partial }_{t}u={\rho }_{\lambda }(x)u{\partial }_x^{2}u+{\rho }_{\lambda }(x)g(x)u$ on the…