We study a linear singular first-order integro-differential Cauchy problems in Banach spaces. Singular here means that the integro differential equation is not in normal form neither can it be reduced to such a form. We generalize to this context some existence and uniqueness theorems known for differential equations. Particular attention is given to single out the optimal regularity properties of solutions as well as to point out several explicit applications related tosingular partial integrodifferential of parabolic type.
Singular integro-differential equations of parabolic type / A. Favini, A. Lorenzi, H. Tanabe. - In: ADVANCES IN DIFFERENTIAL EQUATIONS. - ISSN 1079-9389. - 7:7(2002), pp. 769-798.
Singular integro-differential equations of parabolic type
A. LorenziSecondo
;
2002
Abstract
We study a linear singular first-order integro-differential Cauchy problems in Banach spaces. Singular here means that the integro differential equation is not in normal form neither can it be reduced to such a form. We generalize to this context some existence and uniqueness theorems known for differential equations. Particular attention is given to single out the optimal regularity properties of solutions as well as to point out several explicit applications related tosingular partial integrodifferential of parabolic type.
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