Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-28T07:53:02.842Z Has data issue: false hasContentIssue false
  • English
  • Français

Nonlinear parabolic problems in unbounded domains

Published online by Cambridge University Press:  14 November 2011

Guy Mahler
Guy Mahler
Affiliation:
Mathematics Department, Swiss Federal Institute of Technology, Zurich
Get access Rights & Permissions [Opens in a new window]

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
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 82 , Issue 3-4 , 1979 , pp. 201 - 209
Copyright
Copyright © Royal Society of Edinburgh 1979

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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), 1299–1302.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), 261–278.CrossRefGoogle Scholar
4Edmunds, D. E. and Evans., W. D.Elliptic and degenerate-elliptic operators in unbounded domains. Ann. Scuola Norm. Sup. Pisa 27 (1973), 591–640.Google Scholar
5Edmunds, D. E. and Webb., J. R. L.Quasilinear elliptic problems in unbounded domains. Proc. Roy. Soc. London Ser. A 334 (1973), 397–410.Google Scholar
6Hess., P.Problèmes aux limites non linéaires dans des domaines non bornés. C.R. Acad. Sci. Paris, Ser. A 281 (1975), 555–557.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), 155–175.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