Well posedness for evolution inclusions. (1994)

• Record Type: Journal Article
• Authors: Balachandran, K.; Anguraj, A.
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 7:Number 4(1994)
• Page Start: 537
• Page End: 544
• Publication Date: 1994
• Subjects: well-posedness -- evolution inclusion -- mild solution; Mathematical models -- Periodicals; Computer simulation -- Periodicals; Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Computer simulation; Mathematical models; Applied Mathematics; Periodicals; Electronic journals; 519.22
• DOI: 10.1155/S1048953394000419
• Languages: English
• ISSNs: 1048-9533

Abstract

Abstract : We prove the existence of a continuous selection of the multivalued map φ → Φ ( φ ) which is the set of all mild solutions of the evolution inclusion x ( t ) ∈ A x ( t ) + F ( t, x ( t ) ) + ∫ 0 t h ( t − s ) g ( x ( s ) ) d s x ( 0 ) = φ . Here F is a multivalued map, Lipschitzian with respect to x, and A is the infinitesimal generator of a C 0 -semigroup.