Evolution Problems involving non-stationary Operators between two Banach Spaces II. Ancillary results
- 1 January 1985
- journal article
- research article
- Published by Taylor & Francis in Quaestiones Mathematicae
- Vol. 8 (3) , 199-229
- https://doi.org/10.1080/16073606.1985.9631913
Abstract
This paper is a direct continuation of the first paper in this series[Quaestiones Math. 8 (1985), no. 2,], which deals Kith the evolution problem [B(t)u(t)]' = A(t)u(t), Bu(0) = y. whereas in the first paper existence and uniqueness results were presented, this paper contains the ancillary results formulated in the first paper. These results describe the properties of B(t)-evolutions with non-stationary generating pairs, as well as of the solution operator of [B(t)u(t)]' = Au, Bu(0) = y. The notation of the first paper is assumed throughout and is used without further note. Citation of results from the first paper is made by equation number. The numbering of this paper follows that of the first paper in sequence.Keywords
This publication has 10 references indexed in Scilit:
- A semilinear Sobolev evolution equation in a Banach spacePublished by Elsevier ,2004
- Linear evolution equations in two Banach spacesProceedings of the Royal Society of Edinburgh: Section A Mathematics, 1982
- The sobolev equation, iApplicable Analysis, 1975
- Existence and Representation Theorems for a Semilinear Sobolev Equation in Banach SpaceSIAM Journal on Mathematical Analysis, 1972
- Weak solutions of nonlinear evolution equations of Sobolev-Galpern typeJournal of Differential Equations, 1972
- Local regularity of solutions of Sobolev-Galpern partial differential equationsPacific Journal of Mathematics, 1970
- Partial differential equations of Sobolev-Galpern typePacific Journal of Mathematics, 1969
- Functional AnalysisPublished by Springer Nature ,1965
- Equations Differentielles OperationnellesPublished by Springer Nature ,1961
- Evolutional equations of parabolic typeProceedings of the Japan Academy, Series A, Mathematical Sciences, 1961