Singular integro-differential equations of parabolic type. (English) Zbl 1033.45010

Favini, Angelo; Lorenzi, Alfredo; Tanabe, Hiroki

Adv. Differ. Equ. 7, No. 7, 769-798 (2002).

Summary: We study 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 to singular partial integro-differential of parabolic type.

MSC:

45N05	Abstract integral equations, integral equations in abstract spaces
45J05	Integro-ordinary differential equations
45E10	Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type)
45K05	Integro-partial differential equations

Keywords:

initial value problem; singular integro-differential equations of parabolic type; Cauchy problems in Banach spaces; existence; uniqueness