IJPAM: Volume 113, No. 4 (2017)

Title

ON THE EXISTENCE OF A NONTRIVIAL SOLUTION
OF THE HOMOGENEOUS BOUNDARY VALUE PROBLEM
FOR THE BURGERS EQUATION

Authors

Meiramkul M. Amangaliyeva$^1$, Muvasharkhan T. Jenaliyev$^2$,
Murat I. Ramazanov$^3$
$^{1,2}$Institute of Mathematics and Mathematical Modeling
Almaty, KAZAKHSTAN
$^3$Institute of Applied Mathematics
Karaganda, KAZAKHSTAN
$^3$Buketov Karaganda Stated University
Karaganda, KAZAKHSTAN

Abstract

Research of the Burgers equation has a long history. In work of Y. Benia, B.-K. Sadallah in the Sobolev classes there are results on the existence, uniqueness and regularity for the solution to the Burgers equation in non-cylindrical (non-degenerating) domain, that can be converted into a rectangular domain by a regular replacement of the independent variables. The authors point out that the development of the results of Y. Benia, B.-K. Sadallah for the case of the degenerating domain will be considered in the future. The goal of our work is: to show that the homogeneous boundary value problem for the Burgers equation in the angular (degenerating) domain along with a trivial solution may have a nontrivial solution.

History

Received: December 15, 2016
Revised: January 30, 2017
Published: March 30, 2017

AMS Classification, Key Words

AMS Subject Classification: 35K05, 35K20, 35Q35
Key Words and Phrases: Burgers equation, heat equation, boundary value problems, nontrivial solution

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How to Cite?

DOI: 10.12732/ijpam.v113i4.4 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 113
Issue: 4
Pages: 31 - 45


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