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On the existence of weak solutions for quasilinear parabolic initial-boundary value problems

Published online by Cambridge University Press:  14 November 2011

Rüdiger Landes
Affiliation:
Fachbereich Mathematik und Physik der Universität Bayreuth, Postfach 3008, D-8580 Bayreuth, B.R.D.

Synopsis

Structure conditions on a strongly nonlinear operator A(u) are given, under whichthe initial-Dirichlet-boundary value problem for has weak solutions.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 1981

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References

1Brezis, H. and Browder, F. E.. Strongly nonlinear intial boundary value problems. Proc. Nat. Acad. Sci. U.S.A. 76 (1979), 3840.CrossRefGoogle Scholar
2Browder, F. E.. Existence theory for boundary value problems for quasilinear elliptic systems with strongly nonlinear lower order terms. In Partial Differential Equations, Proceedings of Symposia in Pure Mathematics 23 (Berkeley, 1971), 269—286 (Providence, R.I.: Amer. Math. Soc, 1971).Google Scholar
3Landes, R.. Quasilinear elliptic operators and weak solutions of the Euler equation. Manuscripta Math. 27 (1979), 4772.Google Scholar
4Landes, R.. On Galerkin's method in the existence theory of quasilinear ellipticequations. J. Functional Analysis 39 (1980), 123148.Google Scholar
5Martin, R. H. Jr.Nonlinear Operators and Differential Equations in Banach Spaces (New York: Wiley, 1976).Google Scholar
6Morrey, C. B. Jr.Multiple integrals in the calculus of variation (Berlin: Springer, 1969).Google Scholar
7Robert, J.. Inéquations variationelles paraboliques fortement non linéaires. J. Math. Pures Appl. 53 (1974), 299321.Google Scholar
6Robert, J.. Equations d'évolution parabolique fortement non lineaires. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 1 (1974), 247259.Google Scholar