Global Solutions of Inhomogeneous Viscous Hamilton-Jacobi Equations

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Yousefnezhad, Mohsen | 2010

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 41077 (02)
University: Sharif University of Technology
Department: Pure Mathematics
Advisor(s): Hesaaraki, Mahmoud
Abstract:
We consider the following viscous Hamilton-Jacobi Equations for :

The aim of this paper is to investigate relations between:
(i) The existence of global solutions,
(ii) The existence of stationary solutions (with gradient possibly singular on the boundary), and we obtain precise description of these relations. Namely, (i) imply that (ii), and this case all global solutions converge uniformly to unique stationary solutions. In the redial case, we prove converse of this result. Moreover, for certain smooth function we obtain the existence of global classical solutions with gradient blow-up in infinite time. For or for Cauchy problem, we establish similar relations. Our proofs depend on some new gradient estimate solutions and results obtained from maximum principle. Also, as consequence of these estimate, we prove the parabolic Liouvill-type theorem for solutions of in
Keywords:
Viscous Hamilton Equations ; Jacobi Equations ; Global Solution ; Gradient Blow-Up ; Stationary Solution

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