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published_or_final_version / Mechanical Engineering / Master / Master of Philosophy

This work is concerned with an evolution inclusion of a form, in a triple of spaces \V -> H -> V*", where U is a continuous non-decreasing process, M is a locally square-integrable martingale and the operators A (multi-valued) and B satisfy some monotonicity condition, a coercivity condition and a condition on growth in u. An existence and uniqueness theorem is proved for the solutions, using semi-implicit time-discretization schemes. Examples include evolution equations and inclusions driven by square integrable Levy martingales.

by Zheng Yu-kun. / Thesis (M.Ph.)--Chinese University of Hong Kong, 1987. / Includes bibliographies.

Thesis (M. Phil.)--University of Hong Kong, 2008. / Includes bibliographical references (leaf 88-97) Also available in print.

Thesis (Ph.D.)--City University of Hong Kong, 2009. / "Submitted to Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy." Includes bibliographical references (leaves 157-176)

published_or_final_version / abstract / Mechanical Engineering / Master / Master of Philosophy

The theory of semigroups of linear operators forms an integral part of Functional Analysis with substantial applications to many fields of the natural sciences. In this study we are concerned with the application to equations of mathematical physics. The theory of semigroups of bounded linear operators is closely related to the solvability of evolution equations in Banach spaces that model time dependent processes in nature. Well-posed evolution problems give rise to a semigroup of bounded linear operators. However, in many important and interesting cases the problem is ill-posed making it inaccessible to the classical semigroup theory. One way of dealing with this problem is to generalize the theory of semigroups. In this thesis we give an outline of the theory of two such generalizations, namely, C-regularized semigroups and B-bounded semigroups, with the inter-relations between them and show a number of applications to ill-posed problems. / Thesis (Ph.D.)-University of Natal, Durban, 2001.

Thesis (M. Phil.)--University of Hong Kong, 2007. / Title proper from title frame. Also available in printed format.

Thesis (Ph. D.)--Virginia Polytechnic Institute and State University, 1992. / Vita. Abstract. Includes bibliographical references (leaves 52-54). Also available via the Internet.