Rafael Aparicio, Valentin Keyantuo
Abstract:
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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