Abstract
The initial boundary value problems for linear non-autonomous first-order evolution equations are examined. Our assumptions provide a unified treatment which is applicable to many situations, where the domains of the operators may change with t. We study existence, uniqueness and maximal regularity of solutions in Sobolev spaces. In contrast to the previous results, we use only the continuity assumption on the operators in the main part of the equation.
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Acknowledgements
The author was supported by the Russian Foundation for Basic Research (Grant 18-01-00620) and by the Act 211 of the Government of the Russian Federation, contract No. 02.A03.21.0011.
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Pyatkov, S.G. Solvability of initial boundary value problems for non-autonomous evolution equations. J. Evol. Equ. 20, 39–58 (2020). https://doi.org/10.1007/s00028-019-00516-6
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DOI: https://doi.org/10.1007/s00028-019-00516-6
Keywords
- Operator-differential equation
- Cauchy problem
- Non-autonomous evolution equation
- Maximal regularity
- Initial boundary value problem