Hostname: page-component-7479d7b7d-fwgfc Total loading time: 0 Render date: 2024-07-11T23:29:38.691Z Has data issue: false hasContentIssue false
  • English
  • Français

XXII.—A Priori Estimates and Nonlinear Parabolic Equations of Arbitrary Order

Published online by Cambridge University Press:  14 February 2012

D. E. Edmunds  and
C. A. Stuart
D. E. Edmunds
Affiliation:
Mathematics Division, University of Sussex
C. A. Stuart
Affiliation:
Mathematics Division, University of Sussex
Get access Rights & Permissions [Opens in a new window]

Synopsis

In this paper it is shown that the question of the existence of a classical solution of the first initial-boundary value problem for a non-linear parabolic equation may be reduced to the problem of the derivation of suitable a priori bounds.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 69 , Issue 4 , 1972 , pp. 287 - 293
Copyright
Copyright © Royal Society of Edinburgh 1972

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

References to Literature

[1]Agmon, S., Douglis, A. and Nirenberg, L., 1959. ‘Estimates near the boundary for solutions of elliptic differential equations satisfying general boundary conditions, I’, Communs Pure Appi. Math., 12, 623–722.Google Scholar
[2]Browder, F. E., 1966. ‘Topological methods for non-Linear elliptic equations of arbitrary order’, Pacif. J. Math., 17, 17–31.CrossRefGoogle Scholar
[3]Edmunds, D. E. and Peletier, L. A., 1971. ‘Quasilinear parabolic equations’, Annali Scu. Norm. Sup. Pisa, 25, 397–421.Google Scholar
[4]Ladyzhenskaya, O. A. and Ural'tseva, N. N., 1968. Linear and quasilinear elliptic equations. New York: Academic Press.Google Scholar
[5]Ladyzhenskaya, O. A., Ural'tseva, N. N. and Solonnikov, V. A., 1968. ‘Linear and quasi-linear equations of parabolic type’, Am. Math. Soc. Transi., 23.Google Scholar
[6]Leray, J. and Schauder, J., 1934. ‘Topologie et équations fonctionelles’, Annls Scient. Éc. Norm. Sup., Paris, 51, 45–78.CrossRefGoogle Scholar
[7]Levy, P., 1920. ‘Sur les fonctions lignes implicites’, Bull. Soc. Math. Fr., 48, 13–27.CrossRefGoogle Scholar
[8]Serrín, J., 1969. ‘The problem of Dirichlet for quasilinear elliptic differential equations with many independent variables’, Phil. Trans. Roy. Soc, A264, 413–496.Google Scholar
[9]Solonnikov, V. A., 1965. ‘On boundary value problems for linear parabolic systems of differential equations of general form’, Trudy Mat. Inst. V. A. Steklov, 83.Google Scholar