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Nonlinear parabolic problems in unbounded domains

Published online by Cambridge University Press:  14 November 2011

Guy Mahler
Affiliation:
Mathematics Department, Swiss Federal Institute of Technology, Zurich

Extract

We show the existence of weak solutions of nonlinear parabolic partial differential equations in unbounded domains, provided that a variant of the Leray-Lions conditions is satisfied.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 1979

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References

1Adams., R. A.Sobolev Spaces (New York: Academic Press, 1975).Google Scholar
2Berger, M. S. and Schechter, M.. Lp-embeddings and nonlinear eigenvalue problems for unbounded domains. Bull. Amer. Math. Soc. 76(1970), 12991302.CrossRefGoogle Scholar
3Berger, M. S. and Schechter, M.. Embedding theorems and quasilinear elliptic boundary value problems for unbounded domains. Trans. Amer. Math. Soc. 172 (1973), 261278.CrossRefGoogle Scholar
4Edmunds, D. E. and Evans., W. D.Elliptic and degenerate-elliptic operators in unbounded domains. Ann. Scuola Norm. Sup. Pisa 27 (1973), 591640.Google Scholar
5Edmunds, D. E. and Webb., J. R. L.Quasilinear elliptic problems in unbounded domains. Proc. Roy. Soc. London Ser. A 334 (1973), 397410.Google Scholar
6Hess., P.Problèmes aux limites non linéaires dans des domaines non bornés. C.R. Acad. Sci. Paris, Ser. A 281 (1975), 555557.Google Scholar
7Hille, E. and Phillips., R. S.Functional analysis and semi-groups. Colloquium Publs Amer. Math. Soc. 31 (1957).Google Scholar
8Lions., J. L.Sur certaines équations paraboliques non Iinéaires. Bull. Soc: Math. France 93(1965), 155175.Google Scholar
9Lions., J. L.Quelques méthodes de resolution des problèmes aux limites non linéaires (Paris: Dunod, Gauthiers-Villars, 1969).Google Scholar
10Strauss, W. A.. The energy method in nonlinear partial differential equations. Notas Mat. Inst. Mat. Pura Aplic. Rio de Janeiro 47 (1969).Google Scholar