Tesis
Well-Posedness of Degenerate Integro-Differential Equations with Infinite Delay in Banach Spaces
Autor
Aparicio Cuello, Rafael Antonio
Valentin, Keyantuo (Consejero)
Institución
Resumen
We are concerned with a class of degenerate integro-differential equations of
second order in time in Banach spaces. We characterize their well-posedness using
operator valued Fourier multipliers. These equations are important in several applied
problems in physics and material science, especially for phenomena where memory
effects are important. One such domain is viscoelasticity. We focus on the periodic
case and we treat vector-valued Lebesgue, Besov and Trieblel-Lizorkin spaces. We
note that in the Besov case, the results are applicable in particular to the scale
of vector-valued H¨older spaces Cs, 0 < s < 1. The definition of well posedness
we adopt is a modification of the one used so far in the special cases. Thus, our
results have as corollaries those obtained by several authors for first and second
order integro-differential equations in the non-degenerate context.