On Blow-up and Global Existence of Weak Solutions to Cauchy Problem for Some Nonlinear Equation of the Pseudoparabolic Type

被引：0

作者：

Katasheva, I. K. ^{[1
]}

Korpusov, M. O. ^{[1
]}

Panin, A. A. ^{[1
,2
]}

机构：

[1] Lomonosov Moscow State Univ, Fac Phys, Dept Math, Moscow 119991, Russia

[2] RUDN Univ, Peoples Friendship Univ Russia, Moscow 117198, Russia

来源：

MOSCOW UNIVERSITY PHYSICS BULLETIN | 2023年 / 78卷 / 06期

基金：

俄罗斯科学基金会;

关键词：

nonlinear Sobolev type equations; blow-up; local solvability; nonlinear capacity; estimate of the blow-up time;

D O I：

10.3103/S0027134923060097

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We briefly present the results of the investigation of the Cauchy problem for a nonlinear pseudoparabolic equation that is a mathematical generalisation of a certain model in semiconductor theory. The potential theory for the linear part of the equation is elaborated, which demands quite laborious technique, which can be applied for other equations. The properties of the fundamental solution of this linear part are also of interest because its 1st time derivative possesses a singularity. This is not usual for equations of the considered type. Moreover, sufficient conditions for global-in-time solvability are obtained in the paper, as well as sufficient conditions for its finite-time blow-up.

引用

页码：757 / 772

页数：16