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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)
##### Keywords:
natural growth condition; subsolution; supersolution
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##### References:
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