In this work, we prove the existence of global (in time) small data solutions for wave equations with two dissipative terms and with power nonlinearity vertical bar u vertical bar(p) or nonlinearity of derivative type vertical bar u(t)vertical bar(p), in any space dimension n. 1, for supercritical powers p > (p) over bar. The presence of two dissipative terms strongly influences the nature of the problem, allowing us to derive L-r - L-q long time decay estimates for the solution in the full range 1 <= r <= q <= infinity. The optimality of the critical exponents is guaranteed by a nonexistence result for subcritical powers p < <(p)over bar>.
Global small data solutions for semilinear waves with two dissipative terms / Chen, Wenhui; D'Abbicco, Marcello; Girardi, Giovanni. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - 201:2(2021), pp. 529-560. [10.1007/s10231-021-01128-z]
Global small data solutions for semilinear waves with two dissipative terms
Giovanni Girardi
2021-01-01
Abstract
In this work, we prove the existence of global (in time) small data solutions for wave equations with two dissipative terms and with power nonlinearity vertical bar u vertical bar(p) or nonlinearity of derivative type vertical bar u(t)vertical bar(p), in any space dimension n. 1, for supercritical powers p > (p) over bar. The presence of two dissipative terms strongly influences the nature of the problem, allowing us to derive L-r - L-q long time decay estimates for the solution in the full range 1 <= r <= q <= infinity. The optimality of the critical exponents is guaranteed by a nonexistence result for subcritical powers p < <(p)over bar>.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
