Rothe's method for degenerate quasilinear parabolic equations
Local solution of parabolic equations with strongly increasing nonlinearity by the Rothe method
The local solution of a parabolic-elliptic equation with a nonlinear Neumann boundary condition
We investigate a parabolic-elliptic problem, where the time derivative is multiplied by a coefficient which may vanish on time-dependent spatial subdomains. The linear equation is supplemented by a nonlinear Neumann boundary condition with a locally defined, -bounded function . We prove the existence of a local weak solution to the problem by means of the Rothe method. A uniform a priori estimate for the Rothe approximations in , which is required by the assumptions on , is derived by a technique...
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