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Existence results for some quasilinear parabolic equations. (English) Zbl 0705.35066
A quasilinear parabolic equation is considered. Minimal regularity of the data and a natural growth condition are assumed. It is shown that if there exist a subsolution \(\phi\) and a supersolution \(\psi\) such that \(\phi\leq \psi\), then there exists at least one weak solution u such that \(\phi\leq u\leq \psi\). An analogous result is established also for a corresponding unilateral problem.
Reviewer: M.Fila

MSC:
35K55 Nonlinear parabolic equations
35K85 Unilateral problems for linear parabolic equations and variational inequalities with linear parabolic operators
35D05 Existence of generalized solutions of PDE (MSC2000)
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