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
收藏
页码：4490 / 4499
页数：10
相关论文
共 50 条
  • [1] AN INITIAL-BOUNDARY VALUE PROBLEM FOR THE TWO-DIMENSIONAL ROTATING SHALLOW WATER EQUATIONS WITH AXISYMMETRY
    Hu, Yanbo
    Qian, Yating
    DIFFERENTIAL AND INTEGRAL EQUATIONS, 2022, 35 (9-10) : 611 - 640
  • [2] An initial-boundary value problem for the one-dimensional rotating shallow water magnetohydrodynamic equations
    Ye, Jueling
    Guo, Houbin
    Hu, Yanbo
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2023, 527 (01)
  • [3] An initial-boundary value problem for the Maxwell equations
    Yang, Piwen
    Yang, Shuo
    Li, Manli
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2010, 249 (12) : 3003 - 3023
  • [4] Initial-boundary value problem for stochastic transport equations
    Neves, Wladimir
    Olivera, Christian
    STOCHASTICS AND PARTIAL DIFFERENTIAL EQUATIONS-ANALYSIS AND COMPUTATIONS, 2021, 9 (03): : 674 - 701
  • [5] Initial-boundary value problem for stochastic transport equations
    Wladimir Neves
    Christian Olivera
    Stochastics and Partial Differential Equations: Analysis and Computations, 2021, 9 : 674 - 701
  • [6] On Solvability of an Initial-Boundary Value Problem for a Viscoelasticity Model with Fractional Derivatives
    V. G. Zvyagin
    V. P. Orlov
    Siberian Mathematical Journal, 2018, 59 : 1073 - 1089
  • [7] On Solvability of an Initial-Boundary Value Problem for a Viscoelasticity Model with Fractional Derivatives
    Zvyagin, V. G.
    Orlov, V. P.
    SIBERIAN MATHEMATICAL JOURNAL, 2018, 59 (06) : 1073 - 1089
  • [8] The initial-boundary value problem for a strictly hyperbolic equations
    Liu, Dongdong
    Yu, Kangning
    Guo, Lihui
    COMPUTATIONAL & APPLIED MATHEMATICS, 2022, 41 (05)
  • [9] The initial-boundary value problem for a strictly hyperbolic equations
    Dongdong Liu
    Kangning Yu
    Lihui Guo
    Computational and Applied Mathematics, 2022, 41
  • [10] A NOTE ON THE INITIAL-BOUNDARY VALUE PROBLEM FOR CONTINUITY EQUATIONS WITH ROUGH COEFFICIENTS
    Crippa, Gianluca
    Donadello, Carlotta
    Spinolo, Laura V.
    HYPERBOLIC PROBLEMS: THEORY, NUMERICS, APPLICATIONS, 2014, 8 : 957 - 966
12345