Electron. J. Differential Equations, Vol. 2018 (2018), No. 79, pp. 1-31.

Well-posedness of degenerate integro-differential equations in function spaces

Rafael Aparicio, Valentin Keyantuo

We use operator-valued Fourier multipliers to obtain characterizations for well-posedness of a large class of degenerate integro-differential equations of second order in time in Banach spaces. We treat periodic vector-valued Lebesgue, Besov and Trieblel-Lizorkin spaces. We observe that in the Besov space context, the results are applicable to the more familiar scale of periodic vector-valued H\"older spaces. The equation under consideration are important in several applied problems in physics and material science, in particular for phenomena where memory effects are important. Several examples are presented to illustrate the results.

Submitted September 1, 2017. Published March 20, 2018.
Math Subject Classifications: 45N05, 45D05, 43A15, 47D99
Key Words: Well-posedness; maximal regularity; R-boundedness; operator-valued Fourier multiplier; Lebesgue-Bochner spaces; Besov spaces; Triebel-Lizorkin spaces; Holder spaces.

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Rafael Aparicio
University of Puerto Rico, Río Piedras Campus
Statistical Institute and Computerized Information Systems
Faculty of Business Administration
15 AVE Unviversidad STE 1501, San Juan, PR 00925-2535, USA
email: rafael.aparicio@upr.edu
Valentin Keyantuo
University of Puerto Rico, Río Piedras Campus
Department of Mathematics, Faculty of Natural Sciences
17 AVE Universidad STE 1701, San Juan, PR 00925-2537
email: valentin.keyantuo1@upr.edu

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