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 [5] 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.
Singular evolution integro-differential equations with kernels defined on bounded intervals / A. Favini, A. Lorenzi, H. Tanabe. - In: APPLICABLE ANALYSIS. - ISSN 0003-6811. - 84:5(2005), pp. 463-497. [10.1080/00036810410001724418]
Singular evolution integro-differential equations with kernels defined on bounded intervals
A. LorenziSecondo
;
2005
Abstract
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 [5] 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.Pubblicazioni consigliate
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