Long-time existence of solutions to nonlocal nonlinear bidirectional wave equations

Name: Long-time existence of solutions to nonlocal nonlinear bidirectional wave equations
Author: Erbay, Hüsnü Ata, Erbay, Saadet, Erkip, A.

İsim	Long-time existence of solutions to nonlocal nonlinear bidirectional wave equations
Yazar	Erbay, Hüsnü Ata, Erbay, Saadet, Erkip, A.
Basım Tarihi:	2019-05
Basım Yeri	- American Institute of Mathematical Sciences
Konu	Long-time existence, Nonlocal wave equation, Nash-Moser iteration, Improved Boussinesq equation
Tür	Süreli Yayın
Dil	İngilizce
Dijital	Evet
Yazma	Hayır
Kütüphane:	Özyeğin Üniversitesi
Demirbaş Numarası	1078-0947
Kayıt Numarası	01adb138-4d65-4261-b3e4-e7057555bd32
Lokasyon	Natural and Mathematical Sciences
Tarih	2019-05
Örnek Metin	We consider the Cauchy problem defined for a general class of nonlocal wave equations modeling bidirectional wave propagation in a nonlocally and nonlinearly elastic medium whose constitutive equation is given by a convolution integral. We prove a long-time existence result for the nonlocal wave equations with a power-type nonlinearity and a small parameter. As the energy estimates involve a loss of derivatives, we follow the Nash-Moser approach proposed by Alvarez-Samaniego and Lannes. As an application to the long-time existence theorem, we consider the limiting case in which the kernel function is the Dirac measure and the nonlocal equation reduces to the governing equation of one-dimensional classical elasticity theory. The present study also extends our earlier result concerning local well-posedness for smooth kernels to nonsmooth kernels.
DOI	10.3934/dcds.2019119
Cilt	39

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Long-time existence of solutions to nonlocal nonlinear bidirectional wave equations

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

Basım Tarihi 2019-05

Basım Yeri - American Institute of Mathematical Sciences

Konu Long-time existence, Nonlocal wave equation, Nash-Moser iteration, Improved Boussinesq equation

Tür Süreli Yayın

Dil İngilizce

Dijital Evet

Yazma Hayır

Kütüphane Özyeğin Üniversitesi

Demirbaş Numarası 1078-0947

Kayıt Numarası 01adb138-4d65-4261-b3e4-e7057555bd32

Lokasyon Natural and Mathematical Sciences

Tarih 2019-05

Örnek Metin We consider the Cauchy problem defined for a general class of nonlocal wave equations modeling bidirectional wave propagation in a nonlocally and nonlinearly elastic medium whose constitutive equation is given by a convolution integral. We prove a long-time existence result for the nonlocal wave equations with a power-type nonlinearity and a small parameter. As the energy estimates involve a loss of derivatives, we follow the Nash-Moser approach proposed by Alvarez-Samaniego and Lannes. As an application to the long-time existence theorem, we consider the limiting case in which the kernel function is the Dirac measure and the nonlocal equation reduces to the governing equation of one-dimensional classical elasticity theory. The present study also extends our earlier result concerning local well-posedness for smooth kernels to nonsmooth kernels.

DOI 10.3934/dcds.2019119

Cilt 39