Dafermos Regularization of a Modified KdV-Burgers Equation

Geometric singular perturbation theory;Partial differential equations

Taylor, Monique Richardson ; Dr. Xiao-Biao Lin, Committee Member,Dr. Pierre Gremaud, Committee Member,Dr. Michael Shearer, Committee Member,Dr. Stephen Schecter, Committee Chair,Taylor, Monique Richardson ; Dr. Xiao-Biao Lin ; Committee Member ; Dr. Pierre Gremaud ; Committee Member ; Dr. Michael Shearer ; Committee Member ; Dr. Stephen Schecter ; Committee Chair

University:North Carolina State University

关键词: Geometric singular perturbation theory;    Partial differential equations;   

Others  :  https://repository.lib.ncsu.edu/bitstream/handle/1840.16/4034/etd.pdf?sequence=1&isAllowed=y

美国|英语

来源: null

【 摘 要 】

This project involves Dafermos regularization of a partial differential equation of order higher than 2. The modified Korteweg de Vries-Burgers equation isu_T + f(u)_X = alpha u_XX +beta u_XXX,where the flux is f(u) = u^3,alpha> 0, and beta is nonzero. We show the existence of Riemann-Dafermos solutions near a given Riemann solution composed of shock waves using geometric singular perturbation theory. When beta > 0, there is a possibility that the Riemann solution is composed of two shock waves as opposed to one. In addition, we use linearization to study the stability of the Riemann-Dafermos solutions.