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2010•Journal of Fuyang Teachers CollegeRequires access

On (C,α)-resolvent family

Ying Liu

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Abstract

In this paper we introduced a new class of resolvent families i.e.,(C,α)-resolvent families,and then clarified the equivalent relations between the existence of(C,α)-resolvent families and the C-wellposedness of the Volterra equation.Finally,we showed the((C,α)-resolvent is the mild solution of the Volterra equation under some proper conditions and got the corresponding specific expressions.

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What this paper is about

In this paper we introduced a new class of resolvent families i.e.,(C,α)-resolvent families,and then clarified the equivalent relations between the existence of(C,α)-resolvent families and the C-wellposedness of the Volterra equation.Finally,we showed the((C,α)-resolvent is the mild solution of the Volterra equation under some proper conditions and got the corresponding specific expressions.

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Available abstract

In this paper we introduced a new class of resolvent families i.e.,(C,α)-resolvent families,and then clarified the equivalent relations between the existence of(C,α)-resolvent families and the C-wellposedness of the Volterra equation.Finally,we showed the((C,α)-resolvent is the mild solution of the Volterra equation under some proper conditions and got the corresponding specific expressions.

Key concepts: Resolvent, Resolvent formalism, Mathematics, Volterra equations, Class (philosophy), Volterra integral equation, Pure mathematics, Mathematical analysis

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