CAUCHY PROBLEM FOR HYPERBOLIC EQUATIONS OF THIRD ORDER WITH VARIABLE EXPONENT OF NONLINEARITY

被引：0

作者：

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

Kholyavka, O. T. ^{[2
]}

Pukach, P. Ya. ^{[3
]}

Vovk, M. I. ^{[3
]}

机构：

[1] Ivan Franko Natl Univ Lviv, 1 Univ Ska Str, UA-79000 Lvov, Ukraine

[2] Pidstryhach Inst Appl Problems Mech & Math, 3B Naukova Str, UA-79060 Lvov, Ukraine

[3] Lviv Polytech Natl Univ, 12 Bandera Str, UA-79013 Lvov, Ukraine

来源：

CARPATHIAN MATHEMATICAL PUBLICATIONS | 2020年 / 12卷 / 02期

关键词：

nonlinear hyperbolic equation; Cauchy problem; variable exponent of nonlinearity; Lebesgue space with variable exponent; PARABOLIC EQUATIONS; BLOW-UP; EXISTENCE;

D O I：

10.15330/cmp.12.2.419-433

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We investigate weak solutions of the Cauchy problem for the third order hyperbolic equations with variable exponent of the nonlinearity. The problem is considered in some classes of functions namely in Lebesgue spaces with variable exponents. The sufficient conditions of the existence and uniqueness of the weak solutions to given problem are found.

引用

页码：419 / 433

页数：15

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