TY - JOUR
T1 - Global existence of solutions for a weakly coupled system of semilinear damped wave equations
AU - Nishihara, Kenji
AU - Wakasugi, Yuta
PY - 2015
Y1 - 2015
N2 - In this paper, we consider the Cauchy problem for a weakly coupled system of semilinear damped wave equations. We prove the global existence of solutions for small data in the supercritical case for any space dimension. We also give estimates of the weighted energy of solutions and in a special case, we prove an almost optimal estimate. Moreover, in the subcritical case, we give an almost optimal estimate of the lifespan from both above and below.
AB - In this paper, we consider the Cauchy problem for a weakly coupled system of semilinear damped wave equations. We prove the global existence of solutions for small data in the supercritical case for any space dimension. We also give estimates of the weighted energy of solutions and in a special case, we prove an almost optimal estimate. Moreover, in the subcritical case, we give an almost optimal estimate of the lifespan from both above and below.
KW - Critical exponent
KW - Global existence
KW - Lifespan
KW - Semilinear damped wave equation
KW - Weakly coupled system
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U2 - 10.1016/j.jde.2015.05.014
DO - 10.1016/j.jde.2015.05.014
M3 - Article
AN - SCOPUS:84942815823
SN - 0022-0396
VL - 259
SP - 4172
EP - 4201
JO - Journal of Differential Equations
JF - Journal of Differential Equations
IS - 8
ER -