Abstract
In this paper the existence and uniqueness of the global generalized solution and the global classical solution are studied by the Galerkin method, The class of nonlinear wave equations describe the propagation of long waves with the viscosity in the medium with the dispersive effect. It can also be governing the problem of the longitudinal vibration of the 1-D elastic rod.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
An, L.J., Peire, A.: A weakly nonlinear analysis of elasto-plastic-microstructure models. SIAM J. Appl. Math. 55(1), 136–155 (1995)
Chen, G.W., Yang, Z.J.: Existence and nonexistence of global solutions for a class of nonlinear wave equations. Math. Meth. Appl. Sci. 23, 615–631 (2000)
Zhang, H.W., Chen, G.W.: Potential well method for a class of nonlinear wave equa-tions of fourth-order. Acta Mathematica Scientia 23A(6), 758–768 (2003)
Guenther, R.B., Lee, J.W.: Patial Differential Equations of Mathematical Physics and Integral Equations. Prentice Hall, NJ (1988)
Yang, Z.: Global existence asymptotic behavior and blow-up of solutions for a class of nonlinear wave equations with dissipative term. J. Differential Equations 187, 520–540 (2003)
Chen, G.W., Lu, B.: The initial C boundary value problems for a class of nonlinear wave equations with damping term. J. Math. Anal. Appl. 351, 1–15 (2009)
Mázja, V.G.: Sobolev Spaces. Springer, New York (1985)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Lu, B., Zhang, Q. (2011). The Existence and Uniqueness for a Class of Nonlinear Wave Equations with Damping Term. In: Lin, S., Huang, X. (eds) Advances in Computer Science, Environment, Ecoinformatics, and Education. CSEE 2011. Communications in Computer and Information Science, vol 214. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23321-0_83
Download citation
DOI: https://doi.org/10.1007/978-3-642-23321-0_83
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-23320-3
Online ISBN: 978-3-642-23321-0
eBook Packages: Computer ScienceComputer Science (R0)