Local solutions of weakly parabolic quasilinear differential equations
M. Dreher and V. Pluschke
Abstract.
We consider a quasilinear parabolic boundary value problem,
the elliptic part of which degenerates near the boundary.
In order to solve this problem, we
approximate it by a system of linear degenerate elliptic boundary value problems
by means of semidiscretization with respect to time. We use the theory of
degenerate elliptic operators and weighted Sobolev spaces to find
a priori estimates for the solutions of the approximating problems.
These solutions converge to a local solution if the step size of the
time-discretization goes to zero.
It is worth pointing out that we do not require any growth conditions on the
nonlinear coefficients and right-hand side, since we are able to prove
L^\infty-estimates.
Math. Nachr.
198
(1999),
109-129.
The paper is available here:
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