The Local Strong and Weak Solutions for a Generalized Pseudoparabolic Equation

Nan Li

Abstract and Applied Analysis, 2012, vol. 2012, 1-12

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 ð ¶ ( [ 0 , 𠑇 ) ; ð » ð ‘ â‹‚ ð ¶ ( ð ‘… ) ) 1 ( [ 0 , 𠑇 ) ; ð » ð ‘ âˆ’ 1 ( ð ‘… ) ) with ð ‘ > 3 / 2 , while the existence of local weak solutions is proved in the space ð » ð ‘ ( ð ‘… ) with 1 ≤ ð ‘ â‰¤ 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 ð ¶ ( [ 0 , ∞ ) ; ð » ð ‘ â‹‚ ð ¶ ( ð ‘… ) ) 1 ( [ 0 , ∞ ) ; ð » ð ‘ âˆ’ 1 ( ð ‘… ) ) with ð ‘ â‰¥ 2 .

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:568404

DOI: 10.1155/2012/568404

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