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Besov maximal regularity for a class of degenerate integro‐differential equations with infinite delay in Banach spaces
Author(s) -
Aparicio Rafael,
Keyantuo Valentin
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6462
Subject(s) - mathematics , banach space , degenerate energy levels , class (philosophy) , mathematical analysis , c0 semigroup , nonlinear system , differential equation , pure mathematics , physics , quantum mechanics , artificial intelligence , computer science
The theory of operator‐valued Fourier multipliers is used to obtain characterizations for well‐posedness of a large class of degenerate integro‐differential equations of second order in time in Banach spaces. Specifically, we treat the case of vector‐valued Besov spaces on the real line. It is important to note that in particular, the results are applicable to the more familiar scale of vector‐valued Hölder spaces. The equations under consideration are important in several applied problems in physics and material science, in particular for phenomena where memory effects are important. Several models in the area of viscoelasticity, including heat conduction and wave propagation correspond to the general class of integro‐differential equations considered here. The importance of the results is that they can be used to treat nonlinear equations.