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Existence of traveling waves for a class of nonlocal nonlinear equations with bell shaped kernels

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
ID Code:31093
Deposited By:Albert Erkip
Deposited On:14 Mar 2017 15:23
Last Modified:19 Aug 2017 12:34

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