Mathematical Sciences: Topics On Regularity Theory and Free Boundary Problems

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Laws of Conservation of mass, energy and other physical quantities in the study of fluids and materials can be written as partial differential equations. Realistic models generally lead to nonlinear equations which are often degenerately or singularly parabolic, depending on the physical situation. Whereas the linear theory is well established the nonlinear theory is not. This project will study the smoothness and qualitative behavior of solutions to degenerate and singular parabolic equations.