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Volume 16, Issue 1
Initial Boundary Value Problem for a Damped Nonlinear Hyperbolic Equation

Guowang Chen

J. Part. Diff. Eq., 16 (2003), pp. 49-61.

Published online: 2003-02

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  • Abstract
In the paper, the existence and uniqueness of the generalized global solution and the classical global solution of the initial boundary value problems for the nonlinear hyperbolic equation u_{tt} + k_1u_{xxxx} + k_2u_{xxxxt} + g(u_{xx})_{xx} = f(x, t) are proved by Galerkin method and the sufficient conditions of blow-up of solution in finite time are given.
  • Keywords

Nonlinear hyperbolic equation initial boundary value problem global solution blow-up of solution

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@Article{JPDE-16-49, author = {}, title = {Initial Boundary Value Problem for a Damped Nonlinear Hyperbolic Equation}, journal = {Journal of Partial Differential Equations}, year = {2003}, volume = {16}, number = {1}, pages = {49--61}, abstract = { In the paper, the existence and uniqueness of the generalized global solution and the classical global solution of the initial boundary value problems for the nonlinear hyperbolic equation u_{tt} + k_1u_{xxxx} + k_2u_{xxxxt} + g(u_{xx})_{xx} = f(x, t) are proved by Galerkin method and the sufficient conditions of blow-up of solution in finite time are given.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5405.html} }
TY - JOUR T1 - Initial Boundary Value Problem for a Damped Nonlinear Hyperbolic Equation JO - Journal of Partial Differential Equations VL - 1 SP - 49 EP - 61 PY - 2003 DA - 2003/02 SN - 16 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5405.html KW - Nonlinear hyperbolic equation KW - initial boundary value problem KW - global solution KW - blow-up of solution AB - In the paper, the existence and uniqueness of the generalized global solution and the classical global solution of the initial boundary value problems for the nonlinear hyperbolic equation u_{tt} + k_1u_{xxxx} + k_2u_{xxxxt} + g(u_{xx})_{xx} = f(x, t) are proved by Galerkin method and the sufficient conditions of blow-up of solution in finite time are given.
Guowang Chen . (2019). Initial Boundary Value Problem for a Damped Nonlinear Hyperbolic Equation. Journal of Partial Differential Equations. 16 (1). 49-61. doi:
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