Critical Exponents for the Cauchy Problem to the System of Wave Equations with Time or Space Dependent Damping
Vol. 10 No. 3 (2015) P.283~P.309
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.
Critical exponent, Diffusion phenomena, Global existence, Blow up.
MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: Primary 35B33; Secondly 35L55, 35B40.
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Revised : 2015-05-14