We study linear singular first-order integro-differential Cauchy problems in Banach spaces. The adjective “singular” means here that the integro-differential equation is not in normal form neither can it be reduced to such a form. We generalize some existence and uniqueness theorems proved in  for kernels defined on the entire half-line R+ to the case of kernels defined on bounded intervals removing the strict assumption that the kernel should be Laplace-transformable. Particular attention is paid to single out the optimal regularity properties of solutions as well as to point out several explicit applications relative to singular partial integro-differential equations of parabolic and hyperbolic type.
|Titolo:||Singular evolution integro-differential equations with kernels defined on bounded intervals|
LORENZI, ALFREDO (Secondo)
|Parole Chiave:||Abstract linear singular first-order integro-differential equations, Existence and uniqueness results, Maximal regularity of solutions, Linear singular partial integro-differential equations of parabolic type|
|Settore Scientifico Disciplinare:||Settore MAT/05 - Analisi Matematica|
|Data di pubblicazione:||2005|
|Digital Object Identifier (DOI):||10.1080/00036810410001724418|
|Appare nelle tipologie:||01 - Articolo su periodico|