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Über die C2-Kompaktheit der Bahn von Lösungen semflinearer parabolischer Systeme

Published online by Cambridge University Press:  14 November 2011

Reinhard Redlinger
Reinhard Redlinger
Affiliation:
Mathematisches Institut I, Universität Karlsruhe, West Germany
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Synopsis

The semilinear parabolic system ut + A(x, D)u = g(u) in (0, ∞) × Ω, Ω⊂ℝn bounded, u ∈ ℝN, with homogeneous boundary conditions B(x, D)u=0 on (0, ∞)×∂Ω is considered. The non-linearity g is assumed to be locally Lipschitz-continuous. It is shown that the orbit of a bounded regular solution u is relatively compact in .

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 93 , Issue 1-2 , 1982 , pp. 99 - 103
Copyright
Copyright © Royal Society of Edinburgh 1982

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References

1Amann, H.. Invariant sets and existence theorems for semilinear parabolic and elliptic systems. J. Math. Anal. Appl. 65 (1978), 432–467.CrossRefGoogle Scholar
2Hadeler, K. P.. Diffusion in Fisher's population model. Rocky Mountain J. Math. 11 (1981), 39–45.CrossRefGoogle Scholar
3Ladyzhenskaja, O. A., Solonnikov, V. A. and Ural'tseva, N. N.. Linear and quasilinear equations of parabolic type. Amer. Math. Soc. Transl. Math. Monographs, 23. Providence 1968.Google Scholar
4Ladyzhenskaja, O. A. and Ural'tseva, N. N.. Linear and quasilinear elliptic equations (New York: Academic Press, 1968).Google Scholar
5Sobolevskij, P. E.. Equations of parabolic type in a Banach space. Amer. Math. Soc. Transl. (2) 49 (1966), 1–62.Google Scholar
6Walter, W.. Differential and integral inequalities. Ergebnisse der Mathematik und ihrer Grenzgebiete, 55 (Berlin: Springer, 1970).Google Scholar