Well-posedness of degenerate integro-differential equations in function spaces
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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2018-03-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2018/79/abstr.html |
| Summary: | 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. |
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| ISSN: | 1072-6691 |