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A Property of Weak Solutions for Some Parabolic Equations of Higher Order

Published online by Cambridge University Press:  22 January 2016

Lu-San Chen
Lu-San Chen*
Affiliation:
Department of Mathematics, Taiwan Provincial Cheng-Kung University, Tainan and Mathematical Institute, Nagoya University, Nagoya
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Recently Aronson [1] proved the uniqueness property of weak solutions of the initial boundary value problem for second order parabolic equations with discontinuous coefficients. An analogous result to Aronson’s was proved by Kuroda M in the case of some parabolic equations of higher order, where the method due to Aronson [2] plays an essential role. In this paper, under the same idea we shall be concerned with the asymptotic behavior of weak solutions for parabolic equations of higher order of the divergence form, when the data are prescribed on a portion of a time-like surface.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 29 , March 1967 , pp. 57 - 60
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1967

References

[1] Aronson, D. G., On the Green’s function for second order parabolic differential equations with discontinuous coefficients. Bulletin of the American Mathematical Society 69. (1963), pp. 841–847.CrossRefGoogle Scholar
[2] Aronson, D. G., Uniqueness of positive weak solutions of second order parabolic equations. Annales Polonici Mathematici XVI (1965), pp. 285–303.Google Scholar
[3] Chen, L. S., Asymptotic behavior of solutions of parabolic equations of higher order. (to appear in Pacific J. Math.).Google Scholar
[4] Kuroda, T., Note on the uniqueness property of weak solutions of parabolic equations. (to appear in Nagoya Math. J.).Google Scholar