Critical Exponents for the Cauchy Problem to the System of Wave Equations with Time or Space Dependent Damping
by Kenji Nishihara   Yuta Wakasugi  

Vol. 10 No. 3 (2015) P.283~P.309

ABSTRACT

We consider the Cauchy problem for the system of weakly coupled semilinear wave equations with space or time dependent damping. Our aim is to determine the critical exponents, when the coupled similinear terms are polynomial orders and the damping is effective. In fact, the critical exponents are completely determined in the cases of only space dependent damping and only time dependent damping. But, in the case of both space and time dependent damping it remains open, in which the blow-up result is not obtained even for the scalar damped wave equation.

KEYWORDS
Critical exponent, Diffusion phenomena, Global existence, Blow up.

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: Primary 35B33; Secondly 35L55, 35B40.

MILESTONES

Received: 2015-03-16
Revised : 2015-05-14
Accepted: 2015-05-12

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