Parabolic Differential Inequalities in Cones

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Parabolic Differential Inequalities in Cones

Show simple item record Vaughn, Randy en Lakshmikantham, V. en 2010-06-04T13:43:23Z en 2010-06-04T13:43:23Z en 1978-03 en
dc.identifier.uri en
dc.description.abstract In this paper we investigate the theory of parabolic differential inequalities in arbitrary cones. After discussing the fundamental results concerning parabolic inequalities in cones, we prove a result on flow-invariance which is then used to obtain a comparison theorem. This comparison result is useful in deriving upper and lower bounds on solutions of parabolic differential equations in terms of the solutions of ordinary differential equations. We treat the Dirichlet problem in this paper since its theory follows the general pattern of ordinary differential equations and requires less restrictive assumptions. The treatment of Neumann problem, on the other hand, demands stronger smoothness assumptions and depends heavily on strong maximum principle. The study of the corresponding results relative to Newmann problem is discussed elsewhere. en
dc.language.iso en_US en
dc.publisher University of Texas at Arlington en
dc.relation.ispartofseries Technical Report;78 en
dc.subject Dirichlet problem en
dc.subject Neumann problem en
dc.subject Flow-invariance en
dc.subject Parabolic differential inequalities en
dc.subject.lcsh Mathematical analysis en
dc.subject.lcsh Differential equations en
dc.subject.lcsh Mathematics Research en
dc.title Parabolic Differential Inequalities in Cones en
dc.type Technical Report en
dc.publisher.department Department of Mathematics en

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