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|Title: ||Some mathematical studies on general systems of hyperbolic conservation laws|
|Other Titles: ||Dui yi ban shuang qu shou heng lü de yi xie shu xue li lun de yan jiu|
|Authors: ||Jiang, Zaihong (姜在紅)|
|Department: ||Department of Mathematics|
|Degree: ||Doctor of Philosophy|
|Issue Date: ||2010|
|Publisher: ||City University of Hong Kong|
|Subjects: ||Conservation laws (Mathematics)|
Differential equations, Hyperbolic.
|Notes: ||CityU Call Number: QA377 .J53 2010|
iv, 96 leaves 30 cm.
Thesis (Ph.D.)--City University of Hong Kong, 2010.
Includes bibliographical references (leaves -96)
|Abstract: ||This thesis is concerned with the mathematical studies on the general system of
conservation laws. The research in this area has been one of the most important
and challenging fields in mathematics not only because of many unsolved mathematical problems, but also because of its rich physical background and practical
In Chapter 1 we review some basic results on hyperbolic conservation laws.
Our works are all based on or motivated by the classical results in this Chapter.
In the first part of Chapter 2 we introduce a new nonlinear functional which
improves the one given in  and it can be viewed as a better attempt for the
generalized entropy functional for general equations. In the second part of Chapter 2 we give a new measure about the rarefaction waves, and a sharp decay
estimate of the new measure is established for the cubic nonlinear system of conservation laws. In the third part of Chapter 2 we study some decay estimates
in nonlinear hyperbolic system of conservation laws. By introducing a proper
Glimm functional, we obtain some useful decay estimates which are proved helpful in obtaining decay rates of the admissible solutions to nonlinear hyperbolic
conservation laws as t→∞.
Keywords: conservation laws, wave tracing method, Glimm scheme, Glimm
functional, decay rates|
|Online Catalog Link: ||http://lib.cityu.edu.hk/record=b3947528|
|Appears in Collections:||MA - Doctor of Philosophy |
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