Erkip, Albert and Ramadan, Abba Ibrahim (2017) Existence of traveling waves for a class of nonlocal nonlinear equations with bell shaped kernels. (Accepted/In Press)
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Abstract
In this article we are concerned with the existence of traveling wave solutions of a general class of nonlocal wave equations: utt - a^2uxx = (beta* u^p)xx, p > 1. Members of the class arise as mathematical models for the propagation of waves in a wide variety of situations. We assume that the kernel beta is a bell-shaped function satisfying some mild differentiability and growth conditions. Taking advantage of growth properties of bell-shaped functions, we give a simple proof for the existence of bell-shaped traveling wave solutions.
| Item Type: | Article |
|---|---|
| Subjects: | Q Science > QA Mathematics > QA299.6-433 Analysis |
| Divisions: | Faculty of Engineering and Natural Sciences > Basic Sciences > Mathematics Faculty of Engineering and Natural Sciences |
| Depositing User: | Albert Erkip |
| Date Deposited: | 14 Mar 2017 15:23 |
| Last Modified: | 26 Apr 2022 09:41 |
| URI: | https://research.sabanciuniv.edu/id/eprint/31093 |
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- Existence of traveling waves for a class of nonlocal nonlinear equations with bell shaped kernels. (deposited 14 Mar 2017 15:23) [Currently Displayed]
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