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

Volker Pluschke, Frank Weber (1999)

Commentationes Mathematicae Universitatis Carolinae

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 local assumptions on g , is derived by...

The method of fictitious right-hand sides

Milan Práger (1984)

Aplikace matematiky

The paper deals with the application of a fast algorithm for the solution of finite-difference systems for boundary-value problems on a standard domain (e.g. on a rectangle) to the solution of a boundary-value problem on a domain of general shape contained in the standard domain. A simple iterative procedure is suggested for the determination of fictitious right-hand sides for the system on the standard domain so that its solution is the desired one. Under the assumptions that are usual for matrices...

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