Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-20T00:36:45.564Z Has data issue: false hasContentIssue false
  • English
  • Français

On the solutions of the first boundary value problem for the linear parabolic equations

Published online by Cambridge University Press:  14 November 2011

Eugenio Sinestrari  and
Wolf von Wahl
Eugenio Sinestrari
Affiliation:
Dipartimento di Matematica, Universita di Roma I, P. Aldo Moro 2, I-00185 Roma, Italy
Wolf von Wahl
Affiliation:
Mathematisches Institut, Universität Bayreuth, Postfach 101251, D-8580 Bayreuth, Germany
Get access Rights & Permissions [Opens in a new window]

Synopsis

The first boundary value problem for a linear second order parabolic equation is studied under the assumption that the inhomogeneous term is continuous in space and time and Hölder-continuous only with respect to the space variables.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 108 , Issue 3-4 , 1988 , pp. 339 - 355
Copyright
Copyright © Royal Society of Edinburgh 1988

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

1Bers, L., John, F. and Schechter, M.. Partial differential equations (New York: Interscience, 1964).Google Scholar
2Friedman, A.. Partial differential equations of parabolic type (Englewood Cliffs: Prentice-Hall, 1964).Google Scholar
3Ilin, A. M., Kalashnikov, A. S. and Oleinik, O. A.. Linear equations of the second order of parabolic type. Russian Math. Surveys 17 (1962), 1–143.CrossRefGoogle Scholar
4Kato, T., Perturbation theory for linear operators (Berlin: Springer, Berlin, 1966).Google Scholar
5Ladyzenskaja, O. A., Solonnikov, V. A. and Uralceva, N. N.. Linear and quasilinear equations of parabolic type. Transl. Math. Monographs 23 (Providence: Amer. Math. Soc, 1968).Google Scholar
6Lunardi, A.. Interpolation spaces between domains of elliptic operators and spaces of continuous functions with applications to nonlinear parabolic equations. Math. Nachr. 121 (1985), 295–318.CrossRefGoogle Scholar
7Pogorzelski, W.. Etude d'une fonction de Green et du problème aux limités pour l'equation parabolique normale. Ann. Polon. Math. 4 (1957–1958), 288–207.CrossRefGoogle Scholar
8Sinestrari, E.. On the abstract Cauchy problem of parabolic type in spaces of continuous functions. J. Math. Anal. Appl. 107 (1985), 16–66.CrossRefGoogle Scholar
9Stewart, B.. Generation of analytic semigroups by strongly elliptic operators. Trans. Amer. Math. Soc. 199 (1974), 141–162.CrossRefGoogle Scholar
10von Wahl, W.. Gebrochene Potenzen eines elliptischen Operators und parabolische Differentialgleichungen in Räumen hölderstetiger Funktionen. Nachr. Akad. Wiss. Gottingen Math.-Phys. 11 (1972), 231–258.Google Scholar