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- W3010530904 abstract "We consider the following Cauchy problem for a wave equation with time-dependent damping term b(t)ut and mass term m(t)2u, and a time-dependent non-linearity h = h(t, u): $$displaystyle begin {cases} u_{tt}-Delta u+b(t)u_t+m^2(t)u=h(t,u), & tgeq 0, xin mathbb R^n, u(0,x)=f(x), quad u_t(0,x)=g(x). end {cases} $$Here, we consider an effective time-dependent damping term and a time-dependent mass term, in the case in which the mass is dominated by the damping term, i.e. m(t) = o(b(t)) as t →∞. Under suitable assumptions on the non-linearity h = h(t, u) (Hypothesis 1.3), we prove the global existence of small data solutions in a supercritical range (p>bar p), assuming small data in the energy space (f, g) ∈ H1 × L2." @default.
- W3010530904 created "2020-03-13" @default.
- W3010530904 creator A5001308092 @default.
- W3010530904 date "2020-01-01" @default.
- W3010530904 modified "2023-09-25" @default.
- W3010530904 title "Small Data Solutions for Semilinear Waves with Time-Dependent Damping and Mass Terms" @default.
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- W3010530904 doi "https://doi.org/10.1007/978-3-030-36138-9_14" @default.
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