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The Local Strong and Weak Solutions for a Generalized Pseudoparabolic Equation

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  • Nan Li

Abstract

The Cauchy problem for a nonlinear generalized pseudoparabolic equation is investigated. The well‐posedness of local strong solutions for the problem is established in the Sobolev space C([0, T); Hs(R))⋂ C1([0, T); Hs−1(R)) with s > 3/2, while the existence of local weak solutions is proved in the space Hs(R) with 1 ≤ s ≤ 3/2. Further, under certain assumptions of the nonlinear terms in the equation, it is shown that there exists a unique global strong solution to the problem in the space C([0, ∞); Hs(R))⋂ C1([0, ∞); Hs−1(R)) with s ≥ 2.

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Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:568404
DOI: 10.1155/2012/568404
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