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Theoretical and Numerical Analysis of Shock Waves Propagation in Porous Medium
, Ph.D. Dissertation Sharif University of Technology ; Ahmadi, Mohammad Mehdi (Supervisor) ; Mohammadi, Soheil ($item.subfieldsMap.e)
Abstract
Particulate porous mateials have always been of interest in terms of reducing shock waves effects in different protective applications. Therefore, the physics governing the flow in porous media is especially significant for which different models have been presented by the researchers. The complexities of these media have caused many existing models to be unable to properly predict the behavior of granular media under shock loadings. On the other hand, the complexity of the equations makes the numerical solution of them cumbersome and costly in a way that many researchers do not solve the whole coupled equations and reduce their number. In addition, current high-resolution TVD solutions of...
An optimal Liouville-Type Theorem for Radial Entire Solutions of the Porous Medium Equation with Source
,
M.Sc. Thesis
Sharif University of Technology
;
Hesaraki, Mahmoud
(Supervisor)
Abstract
In this thesis , we consider nonnegative (continuous) weak solutions of the porous medium equation with source , u_t-∆u^m=u^p, and p>m>1 .
Assume that, m>1 and 1< p/m
has no nontrivial, bounded radial solutions u≥0 .
In one space-dimensional, the conclusion of the result mentioned above remains true without the assumption of the radial symmetry. The proof is based on the intersection-comparison arguments , zero number argum- ents and a key step is to show the...
Assume that, m>1 and 1< p/m
has no nontrivial, bounded radial solutions u≥0 .
In one space-dimensional, the conclusion of the result mentioned above remains true without the assumption of the radial symmetry. The proof is based on the intersection-comparison arguments , zero number argum- ents and a key step is to show the...