We consider generalizations of wave maps based on the Skyrme and Adkins-Nappi models of nuclear physics. These models yield nonlinear hyperbolic partial differential equations, for which we consider the question of regularity of solutions. In the case of the Skyrme model, we show that for smooth data of finite energy, the resulting solutions have a conserved energy which does not concentrate, a preliminary step in establishing a global regularity theory. In the case of the Adkins-Nappi model, we obtain a partial result regarding the non-concentration of energy of solutions, which is sufficient to determine many of the properties of solutions.
|Commitee:||Greenleaf, Allan, Jordan, Andrew, Rajeev, Sarada|
|School:||University of Rochester|
|Department:||School of Arts and Sciences|
|School Location:||United States -- New York|
|Source:||DAI-B 74/03(E), Dissertation Abstracts International|
|Subjects:||Applied Mathematics, Mathematics|
|Keywords:||Adkins, Nappi, Non-concentration of energy, Partial differential equations, Skyrme, Topological solitons, Wave maps|
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