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Viability, Invariance, and Nonsmooth PDEs.
Student-Run Research Seminar| Speaker: | Dr. Grant Galbraith, UC Davis |
| Location: | 693 Kerr |
| Start time: | Thu, Feb 8 2001, 10:00AM |
A fruitful approach to analyzing problems in optimization and optimal control has been to formulate them using differential inclusions. A differential inclusion is similar to a differential equation x'(t)=f(t,x(t)), but instead we allow x'(t) to belong to a set of possible values F(t,x(t)). The notions of viability and invariance are then the natural extensions of existence and uniqueness. I will explain what these concepts mean, and then demonstrate how in certain circumstances they lead one to a generalized PDE, the so-called Hamilton-Jacobi equation.