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Title: Theoretical aspects of the Cauchy problem for non-Lipschitz semi-linear parabolic partial differential equations
Author: Meyer, John Christopher
ISNI:       0000 0004 2739 8282
Awarding Body: University of Birmingham
Current Institution: University of Birmingham
Date of Award: 2013
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The aim of this thesis is to provide a generic approach to the study of semi-linear parabolic partial differential equations when the nonlinearity fails to be Lipschitz continuous, but is in the class of Hӧlder continuous functions or the class of upper Lipschitz continuous functions. New results are obtained concerning the well-posedness (in the sense of Hadamard) of the initial value problem, namely, uniqueness and conditional continuous dependence results for upper Lipschitz continuous nonlinearities, and an existence result for Hӧlder continuous nonlinearities. To obtain these results, two new maximum principles have been obtained, for which examples have been provided to exhibit their applications and limitations. Additionally, new derivative estimates of Schauder-type have been obtained. Once the general theory has been established, specific problems are studied in detail. These show how one can apply the general theory, as well as problem specific approaches, to obtain well-posedness results.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics