Displaying similar documents to “Error estimate of approximate solution for a quasilinear parabolic integrodifferential equation in the L p -space”

The local solution of a parabolic-elliptic equation with a nonlinear Neumann boundary condition

Volker Pluschke, Frank Weber (1999)

Commentationes Mathematicae Universitatis Carolinae

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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 - ∂ u / ∂ ν A = g ( · , · , u ) with a locally defined, L r -bounded function g ( t , · , ξ ) . 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 L ∞ , which is required by the assumptions on g , is derived...