Mathematical Sciences: Nonlinear Partial Differential Equations & Their Applications to Evolving Surfaces, Phase Transitions & Stochastic Control

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DMS 9817525SonerThis proposal is on nonlinear analysis with an emphasis on applied mathematicsproblems in material science and financial mathematics. Particular applicationsin material science include modeling grain boundaries, super cooled solidification,and superconductivity. In financial mathematics, applications include pricingcontingent claims in incomplete markets and consumption-investment problems.As an analytical tool, the PI proposes to develop a theory of bounded variationto suitable for vector-valued functions. This theory of functions of type BnVmay have a wide impact in real analysis. In financial mathematics, the PI willlook at problems with portfolio constraints, transaction costs, and models withstocastic volatility.The sophisticated mathematical models arising in the study of new materials and in financial transactions require new methods of mathematics to show that the models are consistent with reality and give reasonable results. The PI will beinvestigating new methods of analysis to apply to such problems as superconductingmaterials and financial models of derivative transactions