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Solution of some non-linear evolutionary equations with boundary degeneration

โœ Scribed by E.I. Tikhomirova

Publisher
Elsevier Science
Year
1983
Weight
419 KB
Volume
23
Category
Article
ISSN
0041-5553

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โœฆ Synopsis

where C.. C, are positive constants. We substitute ul')=v+I:N"x. (!..) ~+ e' N",,f 1 ax" ax" ax,.

for u in (6.1) and group the terms of the same order in I: (by analogy with /9, 10/). Recalling relations (6.5), (6.6), and also estimates (6.10), (6.11) and the a priori estimate for the solution of an elliptic equation in the norm of lV,' (see /8/), we find, with ~1=0(1:'), ~~I/. that p (lIu(')-ullw,'IBnG ยปC. [mes(BnG)] "' I:~"} =0 (e"oo).

whence follows the estimate and hence the theorem.

Corollary. A constant C. exists such that Note 2. Theorem 3 can be extended to the case of more general frame structures.

The author thanks V.L. Berdichevskii for useful discussions.

Translated by D.E.B.

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