Well-posedness of degenerate integro-differential equations in function spaces
Date
2018-03-20
Authors
Aparicio, Rafael
Keyantuo, Valentin
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
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.
Description
Keywords
Well-posedness, Maximal regularity, R-boundedness, Operator-valued Fourier multiplier, Lebesgue-Bochner spaces, Besov spaces, Triebel-Lizorkin spaces, Holder spaces
Citation
Aparicio, R., & Keyantuo, V. (2018). Well-posedness of degenerate integro-differential equations in function spaces. <i>Electronic Journal of Differential Equations, 2018</i>(79), pp. 1-31.
Rights
Attribution 4.0 International