On the well-posedness of a nonlinear pseudo-parabolic equation
https://doi.org/10.1007/s11784-020-00813-5Publisher, magazine: ,
Publication year: 2020
Lưu Trích dẫn Chia sẻAbstract
In this paper we consider the Cauchy problem for the pseudo-parabolic equation: ∂∂t(u+μ(−Δ)s1u)+(−Δ)s2u=f(u),x∈Ω, t>0. Here, the orders s1,s2 satisfy 0<s1≠s2<1 (order of diffusion-type terms). We establish the local well-posedness of the solutions to the Cauchy problem when the source f is globally Lipschitz. In the case when the source term f satisfies a locally Lipschitz condition, the existence in large time, blow-up in finite time and continuous dependence on the initial data of the solutions are given.
Tags: Pseudo-parabolic equation, existence, regularity, asymptotic behavior, blow-up
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