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

Name: Convergence of a linearly regularized nonlinear wave equation to the p-system
Author: Erbay, Hüsnü Ata, Erbay, Saadet, Erkip, A. K.

İsim	Convergence of a linearly regularized nonlinear wave equation to the p-system
Yazar	Erbay, Hüsnü Ata, Erbay, Saadet, Erkip, A. K.
Basım Tarihi:	2023
Basım Yeri	- TÜBİTAK
Konu	Long wave limit, Nonlinear elasticity, Nonlocal, Vanishing dispersion limit
Tür	Süreli Yayın
Dil	İngilizce
Dijital	Evet
Yazma	Hayır
Kütüphane:	Özyeğin Üniversitesi
Demirbaş Numarası	1300-0098
Kayıt Numarası	6126de80-a7e7-47ba-906e-211d7a293a1c
Lokasyon	Natural and Mathematical Sciences
Tarih	2023
Örnek Metin	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

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

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

Basım Tarihi 2023

Basım Yeri - TÜBİTAK

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

Tür Süreli Yayın

Dil İngilizce

Dijital Evet

Yazma Hayır

Kütüphane Özyeğin Üniversitesi

Demirbaş Numarası 1300-0098

Kayıt Numarası 6126de80-a7e7-47ba-906e-211d7a293a1c

Lokasyon Natural and Mathematical Sciences

Tarih 2023

Örnek Metin 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