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

DMS 9817525 Soner这份提案是关于非线性分析的，重点是材料科学和金融数学中的应用数学问题。 在材料科学中的特殊应用包括模拟晶界、过冷凝固和超导性。 在金融数学中，应用包括不完全市场中未定权益的定价和消费投资问题。作为一种分析工具，PI提出发展一种适用于向量值函数的有界变分理论。 这一理论的功能类型BV可能有广泛的影响，在真实的分析。 在金融数学中，PI将研究具有投资组合约束、交易成本和随机波动性的模型问题，在新材料研究和金融交易中出现的复杂数学模型需要新的数学方法来证明模型与实际相符，并给出合理的结果。 PI将研究新的分析方法，以应用于超导材料和衍生交易的金融模型等问题。

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