We study the nonlinear wave equation involving the nonlinear damping term \(u_{i}\left|u_{t}\right|^{m-1}\) and a source term of type \(u|u|^{p-1}\). For \(1<p \leqslant m\) we prove a global existence theorem with large initial data. For \(1<m<p\) a blow-up result is established for sufficiently la
A hybrid legendre tau method for the solution of a class of nonlinear wave equations with nonlinear dissipative terms
โ Scribed by Fatemeh Shakeri; Mehdi Dehghan
- Publisher
- John Wiley and Sons
- Year
- 2010
- Tongue
- English
- Weight
- 473 KB
- Volume
- 27
- Category
- Article
- ISSN
- 0749-159X
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โฆ Synopsis
This article presents a technique based on the hybrid Legendre tau-finite difference method to solve the fourth order wave equation which arises in the elasto-plastic-microstructure models for longitudinal motion of an elasto-plastic bar. Illustrative examples and numerical results obtained using new technique demonstrate that the proposed approach is efficient in treating longitudinal equation of ealsto-plastic bar.
๐ SIMILAR VOLUMES
## Abstract The existence of travelling wave solutions for the heat equation โ~__t__~ __u__ โฮ__u__ = 0 in an infinite cylinder subject to the nonlinear Neumann boundary condition (โ__u__ /โ__n__) = __f__ (__u__) is investigated. We show existence of nontrivial solutions for a large class of nonlin
Building on the method of Kantorovich majorants, we give convergence results and error estimates for the two-step Newton method for the approximate solution of a nonlinear operator equation.