Abstract
We are concerned with the initial value problem governed by generalized Rayleigh–Stokes equations, where the nonlinearity depends on history states and takes values in Hilbert scales of negative order. The solvability and Hölder regularity of solutions are proved using fixed point arguments and embeddings of fractional Sobolev spaces. An application to a related inverse source problem is given.
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Acknowledgements
The authors are grateful to the anonymous referees for their valuable suggestions and comments leading to improvement in the presentation of this paper. The authors would like to thank Hanoi National University of Education for providing a fruitful working environment. This work is funded by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant number 101.02\(-\)2020.07.
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Ke, T.D., Thang, N.N. On Global Solvability and Regularity for Generalized Rayleigh–Stokes Equations with History-Dependent Nonlinearities. Mediterr. J. Math. 20, 107 (2023). https://doi.org/10.1007/s00009-023-02318-0
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DOI: https://doi.org/10.1007/s00009-023-02318-0