| Autor: |
Erbay, H. A., Erbay, S., Erkip, A. |
| Rok vydání: |
2018 |
| Předmět: |
|
| Zdroj: |
Discrete and Continuous Dynamical Systems 39, 2877-2891 (2019) |
| Druh dokumentu: |
Working Paper |
| Popis: |
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. |
| Databáze: |
arXiv |
| Externí odkaz: |
|
