A priori estimates of strong solutions of semilinear parabolic equations期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

首页 | 本学科首页

官方微博 | 高级检索

按检索

A priori estimates of strong solutions of semilinear parabolic equations

Authors:

G G Laptev

Institution:

(1) V. A. Steklov Mathematics Institute, Russian Academy of Sciences, USSR

Abstract:

We study an initial boundary value problem for the semilinear parabolic equation

$\frac{{\partial u}}{{\partial t}} + \sum\limits_{\left| \alpha \right| \leqslant 2b} {a_\alpha } (x,t)D^\alpha u = f(x, t, u, Du,..., D^{2b - 1} u\user2{),}$

where the left-hand side is a linear uniformly parabolic operator of order 2b. We prove sufficient growth conditions on the functionƒ with respect to the variablesu, Du,, D ^2b–1 u, such that the apriori estimate of the norm of the solution in the Sobolev spaceW _p ^2b,1 is expressible in terms of the low-order norm in the Lebesgue space of integrable functionsL _l,m.Translated fromMatematicheskie Zametki, Vol. 64, No. 4, pp. 564–572, October, 1998.In conclusion, the author wishes to thank his scientific adviser, corresponding member of the Russian Academy of Sciences S. I. Pokhozhaev, for setting the problem and useful discussions of the results, and also Ya. Sh. Il'yasov for valuable remarks.This research was supported by the Russian Foundation for Basic Research under grant No. 96-15-96102.

Keywords:

semilinear parabolic equation a priori estimate sufficient growth conditions Lebesgue space of integrable functionsL _l m Sobolev spaceW _p ^2b 1

本文献已被 SpringerLink 等数据库收录！

设为首页 | 免责声明 | 关于勤云 | 加入收藏