Local Solvability and Blow-Up of Classical Solution to Some Initial-Boundary Value Problem for a Nonlinear Equation Governing Ion-Acoustic Waves in a Plasma

被引：0

作者：

Ovsyannikov, E. A. ^{[1
,2
,3
]}

机构：

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

[2] RUDN Univ, Moscow 117198, Russia

[3] Natl Res Nucl Univ MEPhI, Moscow 115409, Russia

来源：

COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS | 2024年 / 64卷 / 10期

关键词：

nonlinear Sobolev-type equations; local solvability; test function; blow-up; blow-up time estimate; HOLDER REGULARITY; CAUCHY-PROBLEMS;

D O I：

10.1134/S0965542524701288

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

An initial-boundary value problem for a Sobolev-type equation from the theory of ion-acoustic plasma waves is considered. The problem is reduced to an equivalent abstract integral equation. The local solvability of the equation is proved using the contraction mapping principle. Next, the bootstrap method is employed to improve the smoothness of the solution. Finally, the test function method with a certain sufficient condition is used to obtain a finite time blow-up result and an upper bound on the blow-up time is found.

引用

页码：2305 / 2319

页数：15

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