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- W3089594043 abstract "The main purpose of this paper is to investigate decay estimates for solutions to the Cauchy problemutt+a1(x)(−Δ)σu+aut=0,u(0,x)=u0(x),ut(0,x)=u1(x)forx∈Rn, as well as the estimates for solutions to the corresponding Cauchy-Dirichlet problem in an exterior domain Ω⊂Rn. Here a is a positive constant. The coefficient a1=a1(x) is supposed to be continuous and positive on the closure Ω‾. The parameter σ∈(0,1) brings to the model the so-called Levi-stable behavior for the corresponding diffusion stochastic process. Finally, we show the global (in time) existence of energy solutions from evolution spaces to the semilinear modelsutt+a1(x)(−Δ)σu+aut=|ut|p,u(0,x)=u0(x),ut(0,x)=u1(x), in domain (0,∞)×Ω with arbitrarily small initial data." @default.
- W3089594043 created "2020-10-08" @default.
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- W3089594043 date "2021-02-01" @default.
- W3089594043 modified "2023-09-25" @default.
- W3089594043 title "Semilinear mixed problems in exterior domains for σ-evolution equations with friction and coefficients depending on spatial variables" @default.
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- W3089594043 doi "https://doi.org/10.1016/j.jmaa.2020.124587" @default.
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