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… Click to show full 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.
Journal Title: Mathematical Methods in the Applied Sciences
Year Published: 2024
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