Asymptotic estimates for a nonlinear wave problem

Cristian Rojas Milla; Alex Pico Amaya

Cristian Rojas Milla Universidad del Atlántico
Alex Pico Amaya Universidad del Atlántico

Palabras clave: Asymptotic solutions, damped wave equation, periodic problems, Sobolev spaces Asymptotic solutions, damped wave equation, periodic problems, Sobolev spaces

Resumen

We study the asymptotic solutions for a nonlinear damped wave problem showing the existence and uniqueness of solutions by contraction

Visitas al artículo

118

Descargas

La descarga de datos todavía no está disponible.

Referencias

Ali Sulaiman F. B. , LeachJ. A., Needham D. J., The Large-Time Solution of Burgers’ Equation with Time-Dependent Coefficients. II. Algebraic Coefficients Studies in Applied Mathematics Volume 137, Issue 3, June 2016

Ball, J. M., Remarks On Blow-up And Nonexistence Theorems For Nonlinear Evolution Equations The Quarterly Journal of Mathematics, Volume 28, Issue 4, Pages 473–486, December 1977

Fujita H., On the blowing up of the Cauchy problem for ut = δu + u 1+κ , J. Fac Sci. Univ. Tokyo (1966), Sect.I.13. 109-124, MR35 6761.

Hayashi N., Kaikina E., Naumkin P., Shishmarev I., Asymptotics for dissipative Nonlinear Equations, Springer, 2006

Hayashi N., Naumkin P., Asymptotic of odd solutions for cubic nonlinear Schr¨odinger equations, Journal of Differential Equationes, Vol. 246, No. 4 pp. 1703- 1722, 2009.

Hayashi N., Naumkin P., Rodriguez-Ceballos J., Asymptotics of solutions to the periodic problem for the nonlinear damped wave equation, Non Linear Differential Equations and Applications (Ed. Zarantonello E.H.), Academic Press 19719, 565-601.

Iorio ´ Junior R. , de Magalhaes Iorio ´ V. , Equa¸co˜es diferenciais parciais: Uma introdu¸c˜ao, Instituto de Matem´atica Pura y Aplicada, CNPq, 1988 (Proyecto Euclides).

Kaikina E.I., Naumkin P.I., Shishmarev I.A., Periodic problem of a model nonlinear evolution equation, Adv. Differ. Equ., 7(2000), No. 5,581-616

Linares F., Ponce G., Introduction to no linear dispersive equations, SpringerVerlag Business media, lcc New York, 2009.

Linares F., Ecuaciones dispersivas no lineales. Caso peri´odico, XX Escuela Venezolana de Matem´aticas, September 2007

Leach, J. A., The Large-Time Solution of Burgers’ Equation with Time-Dependent Coefficients. I. The Coefficients Are Exponential Functions Studies in Applied Mathematics Volume 136, Issue 2, October 2015

Marsden, Jerold. E, Hugues, Thomas, J.R, ”Mathematical Foundations of Elasticity”, Prentice-Hall, 1983.

Pazy A., Semi-groups of linear operators and applications to partial differential equations, Applied Mathematical Sciences, V.44 Springer-Verlag, New York, Inc. 1983.