Solvability of the First Initial-boundary Value Problem for the Quasihydrodynamics Equations in the Shallow Water Approximation

被引：0

作者：

Evseev, F. A. ^{[1
,2
]}

Pyatkov, S. G. ^{[1
,3
]}

机构：

[1] Yugra State Univ, Khanty Mansiysk 628012, Russia

[2] Shpilman Res & Analyt Ctr Rat Use Subsoil, Khanty Mansiysk 628007, Russia

[3] Acad Sci Republ Sakha Yakutia, Yakutsk, Russia

来源：

LOBACHEVSKII JOURNAL OF MATHEMATICS | 2024年 / 45卷 / 09期

关键词：

initial-boundary value problem; quasi-hydrodynamic system; a priori estimate; regular solution; shallow water approximation; CLASSICAL-SOLUTIONS; EXISTENCE;

D O I：

10.1134/S1995080224605083

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The unique solvability of an analog of the first initial boundary value problem for the quasihydrodynamics equations in the shallow water approximation is established under certain conditions on the data. A solution is regular , i.e., all generalized derivatives occurring in the equation are summable to some power. The proof relies on a priori estimates and the contraction mapping principle.

引用

页码：4490 / 4499

页数：10

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