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Estimates on the support of the solutions of some nonlinear elliptic and parabolic problems

Published online by Cambridge University Press:  14 November 2011

J. I. Díaz  and
M. A. Herrero
J. I. Díaz
Affiliation:
Departamento de Ecuaciones Funcionales, Facultad de Matematicas, Universidad Complutense, Madrid 3, Spain
M. A. Herrero
Affiliation:
Departamento de Ecuaciones Funcionales, Facultad de Matematicas, Universidad Complutense, Madrid 3, Spain
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Synopsis

We obtain existence and uniqueness of solutions with compact support for some nonlinear elliptic and parabolic problems including the equations of one-dimensional motion of a non-newtonian fluid. Precise estimates for the support of these solutions are obtained, and the optimality of our hypotheses is discussed.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 89 , Issue 3-4 , 1981 , pp. 249 - 258
Copyright
Copyright © Royal Society of Edinburgh 1981

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References

1Benilan, P.. Equations d'evolution dans un espace de Banach quelconque et applications. These d'Etat, Orsay (1972).Google Scholar
2Benilan, P.. Operateurs accretifs et semigroupes dans les Lp (1≦p≦∞). Japan—France Seminar 1976, Fujita, H. ed. (Tokyo: Japan Soc. for the Prom, of Science, 1978).Google Scholar
3Benilan, P., Brezis, H. and Crandall, M. G.. A semilinear equation in L1(ℝ). Ann. Scuola Norm. Sup. Pisa 2 (1975), 523–555.Google Scholar
4Brezis, H.. Operateurs maximaux monotones et semigroups de contractions dans les espaces de Hilbert. Notas de Matematica 50 (Amsterdam: North Holland, 1973).Google Scholar
5Brezis, H. and Friedman, A.. Estimates on the support of solutions of parabolic variational inequalities. Illinois J. Math. 20 (1976), 32–99.CrossRefGoogle Scholar
6Brack, R.. Asymptotic convergence of nonlinear contraction semigroups in Hilbert Spaces. J. Functional Analysis 18 (1975), 15–26.CrossRefGoogle Scholar
7Diaz, J. I.. Solutions with compact support of some degenerate parabolic problems. Nonlinear Analysis 3 (1979), 813–847.Google Scholar
8Diaz, J. I.. Soluciones con soporte compacto para ciertos problemas semilineales. Collect. Math. 30 (1979), 141–179.Google Scholar
9Diaz, J. I.. Anulacion de soluciones para ciertos problemas parabolicos no lineales. Ret). Real Acad. d. Exact. Fís. Natur. Madrid 72 (1978), 613–616.Google Scholar
10Diaz, J. I. and Herrero, M. A.. Proprietes de support compact pour certaines equations elliptiques et paraboliques non lineaires. C. R. Acad. Sci. Paris 286 (1978), 815–817.Google Scholar
11Evans, L. C.. Application of nonlinear semigroup theory to certain partial differential equations. In Nonlinear evolution equations, Crandall, M. G. ed. (New York: Academic Press, 1978).Google Scholar
12Herrero, M. A.. Comportamiento de las soluciones de ciertos problemas no lineales sobre dominios no acotados (Tesis Doctoral, Univ. Complutense de Madrid, 1979).Google Scholar
13Kalashnikov, A. S.. On the concept of finite speed signal propagation. Uspehi Mat. Nauk 20 (1979), 199–200 (In Russian).Google Scholar
14Lions, J. L.. Quelques méthodes de résolution des problémes aux limites non linéaires (Paris: Dunod, 1969).Google Scholar
15Martinson, L. K. and Pavlov, K. B.. The effect of magnetic plasticity in non-newtonian fluids. Magnit. Gidrodinamika 3 (1969), 69–75.Google Scholar
16Martinson, L. K. and Pavloc, K. B.. Unsteady shear flows of a conducting fluid with a rheological power law. Mapiit. Gidrodinamika 2 (1970), 50–58.Google Scholar
17Oleinik, O. A., Kalashnikov, A. S. and Yulin, C.. The Cauchy problem and boundary problems for equations of the type of nonstationary filtration. Izv. Akad. Nauk SSSR Ser. Mat. 22 (1958), 667–704 (In Russian).Google Scholar