Back to Search

Convergence of a linearly regularized nonlinear wave equation to the p-system

Title	Convergence of a linearly regularized nonlinear wave equation to the p-system
Author	Erbay, Hüsnü Ata, Erbay, Saadet, Erkip, A. K.
Publication Date:	2023
Publication Place	- TÜBİTAK
Subject	Long wave limit, Nonlinear elasticity, Nonlocal, Vanishing dispersion limit
Type	Periodical
Language	English
Digital	Yes
Manuscript	No
Library:	Özyeğin University
Library Asset ID	1300-0098
Record ID	6126de80-a7e7-47ba-906e-211d7a293a1c
Library Location	Natural and Mathematical Sciences
Date	2023
Sample Text	We consider a second-order nonlinear wave equation with a linear convolution term. When the convolution operator is taken as the identity operator, our equation reduces to the classical elasticity equation which can be written as a p-system of first-order differential equations. We first establish the local well-posedness of the Cauchy problem. We then investigate the behavior of solutions to the Cauchy problem in the limit as the kernel function of the convolution integral approaches to the Dirac delta function, that is, in the vanishing dispersion limit. We consider two different types of the vanishing dispersion limit behaviors for the convolution operator depending on the form of the kernel function. In both cases, we show that the solutions converge strongly to the corresponding solutions of the classical elasticity equation.
DOI	10.55730/1300-0098.3407
Cilt	47

View in source Özyeğin University Özyeğin University - Historical works, archives, and periodicals search engine

Özyeğin University

Convergence of a linearly regularized nonlinear wave equation to the p-system

Author Erbay, Hüsnü Ata, Erbay, Saadet, Erkip, A. K.

Publication Date 2023

Publication Place - TÜBİTAK

Subject Long wave limit, Nonlinear elasticity, Nonlocal, Vanishing dispersion limit

Type Periodical

Language English

Digital Yes

Manuscript No

Library Özyeğin University

Library Asset ID 1300-0098

Record ID 6126de80-a7e7-47ba-906e-211d7a293a1c

Library Location Natural and Mathematical Sciences

Date 2023

Sample Text We consider a second-order nonlinear wave equation with a linear convolution term. When the convolution operator is taken as the identity operator, our equation reduces to the classical elasticity equation which can be written as a p-system of first-order differential equations. We first establish the local well-posedness of the Cauchy problem. We then investigate the behavior of solutions to the Cauchy problem in the limit as the kernel function of the convolution integral approaches to the Dirac delta function, that is, in the vanishing dispersion limit. We consider two different types of the vanishing dispersion limit behaviors for the convolution operator depending on the form of the kernel function. In both cases, we show that the solutions converge strongly to the corresponding solutions of the classical elasticity equation.

DOI 10.55730/1300-0098.3407

Cilt 47