the local strong and weak solutions for a generalized pseudoparabolic equation
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2012
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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 ๐ถ([0,๐);๐ป๐ โ๐ถ(๐
))1([0,๐);๐ป๐ โ1(๐
)) with ๐ >3/2, while the existence of local weak solutions is proved in the space ๐ป๐ (๐
) with 1โค๐ โค3/2. 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 ๐ถ([0,โ);๐ป๐ โ๐ถ(๐
))1([0,โ);๐ป๐ โ1(๐
)) with ๐ โฅ2.
| Reference Key |
li2012abstractthe
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|---|---|
| Authors | ;Nan Li |
| Journal | science and technology of advanced materials |
| Year | 2012 |
| DOI |
10.1155/2012/568404
|
| URL | |
| Keywords |
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