Global existence of solutions for damped wave equations with nonlinear memory

Abstract

This article studies the Cauchy problem for the damped wave equation with nonlinear memory. For a noncompactly supported initial data with small energy, global existence and asymptotic behaviour of solutions are obtained when 1 ≤ n ≤ 3. This result generalized the previous result by Fino [Critical exponent for damped wave equations with nonlinear memory, Nonlinear Anal. 74 (2011), pp. 5495–5505], which dealt with the solution with compactly supported initial data.

Keywords:

• nonlinear damped wave equation
• global existence
• noncompactly supported initial data
• large time asymptotic behaviour

AMS Subject Classifications::

• 35L15
• 35L70

Acknowledgements

This research is supported by the National Natural Science Foundation of PR China (No. 71003082) and the Fundamental Research Funds for the Central Universities (SWJTU12CX61 and SWJTU12ZT13).