Sun Siu-wing. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (leaves 50-51). / Abstracts in English and Chinese. / Acknowledgments --- p.i / Abstract --- p.ii / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Equation without viscosity --- p.5 / Chapter 3 --- Equation with standard viscosity --- p.8 / Chapter 3.1 --- "Particular convective flux, f(x) =u2" --- p.8 / Chapter 3.2 --- Convex convective flux --- p.10 / Chapter 4 --- Equation with monotonic dissipative flux --- p.11 / Chapter 4.1 --- Large initial data --- p.12 / Chapter 4.2 --- Small initial data --- p.19 / Chapter 4.3 --- Unbounded dissipative flux --- p.28 / Chapter 5 --- Equation with non-monotonic dissipative flux --- p.31 / Chapter 5.1 --- Large initial data --- p.32 / Chapter 5.2 --- Small initial data --- p.37 / Chapter 6 --- Comparison and conclusions --- p.39 / Appendices --- p.42 / Chapter A --- Hopf-Cole transformation --- p.42 / Chapter B --- Dirichlet problem --- p.45 / Bibliography --- p.50

Thesis (Ph. D.)--University of Chicago, Department of Mathematics, June 2001. / Includes bibliographical references. Also available on the Internet.

Thesis (Ph. D.)--University of Texas at Austin, 2002. / Vita. Includes bibliographical references. Available also from UMI Company.

In this thesis, we establish the asymptotic analysis of the singularly perturbed reaction diffusion equation [cataloger unable to transcribe mathematical equations].... Our results establish the specific dependency on the coefficients of this equation and the size of the parameter [delta] with respect to [epsilon]. The analyses include equation subject to Dirichlet and Neumann boundary conditions. In both cases, the solutions u[superscript epsilon] converge locally uniformally to the equilibria of the reaction term f. We characterize the limiting behavior of the solutions through the viscosity solution of a variational inequality. To construct the coefficients defining the variational inequality, we apply concepts developed for the homogenization of elliptic operators. In chapter two, we derive the convergence results in the Neumann case. The third chapter is dedicated to the analysis of the Dirichlet case. / text

Not available / text

Thesis (Ph. D.)--University of Texas at Austin, 2007. / Vita. Includes bibliographical references.

published_or_final_version / Physics / Doctoral / Doctor of Philosophy

Thesis (Ph. D.)--University of Missouri-Columbia, 1996. / Typescript. Vita. Includes bibliographical references (leaves 115-118). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 1996. / Typescript. Vita. Includes bibliographical references (leaves 115-118). Also available on the Internet.

Thesis (PhD (Mathematics and Applied Mathematics)) -- University of Pretoria, 2007. / Abstract in English. Includes bibliographical references.