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- Title
Final value problem governed by a class of time‐space fractional pseudo‐parabolic equations with weak nonlinearities.
- Authors
Dinh Ke, Tran; Bao Ngoc, Tran; Huy Tuan, Nguyen
- Abstract
We study the final value problem involving a class of semilinear fractional pseudo‐parabolic equations, where the nonlinearity probably takes values in fractional Sobolev spaces. By establishing some estimates for resolvent operators and employing the embedding related to Hilbert scales and fractional Sobolev spaces, we are able to obtain the existence and uniqueness result to the mentioned problem. In addition, the behavior of solutions at initial time is analyzed with respect to the final data. It will be shown that various cases of the nonlinearity functions meet our setting, including functions with gradient term.
- Subjects
SOBOLEV spaces; RESOLVENTS (Mathematics); EQUATIONS
- Publication
Mathematical Methods in the Applied Sciences, 2024, Vol 47, Issue 6, p5307
- ISSN
0170-4214
- Publication type
Article
- DOI
10.1002/mma.9866