Sobolev型模型方程Cauchy问题中临界指数“瞬时爆破”与“局部溶解度”的关系

IF 0.8 3区数学 Q2 MATHEMATICS

Izvestiya Mathematics Pub Date : 2021-01-01 DOI:10.1070/IM8949

M. O. Korpusov, A. A. Panin, A. Shishkov

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引用次数: 5

摘要

考虑一类三阶偏微分方程的柯西问题，其非线性形式为:证明了柯西问题中对于一类大的初值函数没有局部时弱解，而当3/2$?b>存在一个局部弱解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On the critical exponent “instantaneous blow-up” versus “local solubility” in the Cauchy problem for a model equation of Sobolev type

We consider the Cauchy problem for a model partial differential equation of order three with a non-linearity of the form . We prove that when the Cauchy problem in has no local-in-time weak solution for a large class of initial functions, while when 3/2$?> there is a local weak solution.

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来源期刊

Izvestiya Mathematics 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The Russian original is rigorously refereed in Russia and the translations are carefully scrutinised and edited by the London Mathematical Society. This publication covers all fields of mathematics, but special attention is given to: Algebra; Mathematical logic; Number theory; Mathematical analysis; Geometry; Topology; Differential equations.