Nonlinear evolution equations on Banach space. (1991)

• Record Type: Journal Article
• Authors: Ahmed, N. U.
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 4:Number 3(1991)
• Page Start: 187
• Page End: 202
• Publication Date: 1991
• Subjects: evolution equations -- deterministic -- stochastic -- semilinear -- quasilinear -- integral equations -- semigroup theory -- Wiener process; 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/S1048953391000151
• Languages: English
• ISSNs: 1048-9533

Abstract

Abstract : In this paper we consider the questions of existence and uniqueness of solutions of certain semilinear and quasilinear evolution equations on Banach space. We consider both deterministic and stochastic systems. The approach is based on semigroup theory and fixed point theorems. Our results allow the nonlinear perturbations in all the semilinear problems to be bounded or unbounded with reference to the base space, thereby increasing the scope for applications to partial differential equations. Further, quasilinear stochastic evolution equations seemingly have never been considered in the literature.