Breakdown of solutions to $\square u+u_t=|u|^{1+\alpha}$

Tatsien Li; Yi Zhou

doi:10.3934/dcds.1995.1.503

Article Contents

1995, Volume 1, Issue 4: 503-520. Doi: 10.3934/dcds.1995.1.503

This issue Previous Article Homogenization of time-dependent systems with Kelvin-Voigt damping by two-scale convergence Next Article On the existence of solutions of the Cauchy problem for porous medium equations with radon measure as initial data

Breakdown of solutions to $\square u+u_t=|u|^{1+\alpha}$

Tatsien Li^1, and
Yi Zhou^2,

1.
School of Mathematical Sciences, Fudan University, Han Dan Road 220, Shanghai 200433
2.
Department of Mathematics, Fudan University, Key Laboratory of Mathematics for Nonlinear Sciences (Fudan University), Ministry of Education of China, Shanghai 200433

Received: October 31, 1994

Published: September 1995

Abstract Related Papers Cited by

Abstract

In the paper we give an upper bound for the life-span of the mild solution to the Cauchy problem for semilinear equations $\square u+u_t=|u|^{1+\alpha}$ ($\alpha >0,$ constant) with certain small initial data. This shows the sharpness of the lower bound obtained in [2] on the life-span of classical solutions to the Cauchy problem for fully nonlinear wave equations with linear dissipation with small initial data.

Keywords:

Blow up,
life-span,
nonlinear wave equation with dissipation.

Mathematics Subject Classification: 35L70, 35L05, 35L15.

Citation:

Article Metrics

HTML views() PDF downloads(226) Cited by(0)

Breakdown of solutions to $\square u+u_t=|u|^{1+\alpha}$

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

Breakdown of solutions to $\square u+u_t=|u|^{1+\alpha}$

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content