## Abstract In this paper, we consider a family of finite difference operators {__Ah__ }~__h__ >0~ on discrete __L__ ~__q__~ βspaces __L__ ~__q__~ (β^__N__^ ~__h__~ ). We show that the solution __u__ ~__h__~ to __u__ β²~__h__~ (__t__) β __A__ ~__h__~ __u__ ~h~(__t__) = __f__ ~__h__~ (__t__), __t__
Maximal regularity of typeLpfor abstract parabolic Volterra equations
β Scribed by Rico Zacher
- Publisher
- Springer
- Year
- 2005
- Tongue
- English
- Weight
- 278 KB
- Volume
- 5
- Category
- Article
- ISSN
- 1424-3199
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π SIMILAR VOLUMES
We introduce a two-kernel dependent family of strong continuous operators defined in a Banach space, which allows us to consider in an unified treatment the notions of, among others, C -semigroups of operators, cosine families, n-times 0 integrated semigroups, resolvent families and k-generalized so
A ΠΈ g C 0, T , L L D A 0 , X and construct the corresponding evolution family on the underlying Banach space X. Our proofs are based on the operator sum method and the use of evolution semigroups. The results are applied to parabolic partial differential equations with continuous coefficients.