Envelope viscosity solutions of first- and second-order PDEs with u-dependence |
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Authors: | Emmanuel N Barron Robert R Jensen |
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Institution: | 1. Department of Mathematics and Statistics, Loyola University Chicago, Chicago, IL, USABarron:ebarron@luc.edu;3. Department of Mathematics and Statistics, Loyola University Chicago, Chicago, IL, USA |
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Abstract: | General envelope methods are introduced which may be used to embed equations with u-dependence into equations without solution dependence. Furthermore, these methods present a rigorous way to consider so-called nodal solutions. That is, if w(t,x,z) is the viscosity solution of some pde, the nodal solution of an associated pde is a function u(t,x) so that w(t,x,u(t,x)) = 0. Examples are given to first- and second-order pdes arising in optimal control, differential games, minimal time problems, scalar conservation laws, geometric-type equations, and forward backward stochastic control. |
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Keywords: | Bellman envelope Forward Backward Isaacs Nodal nonlinear partial differential equation viscosity solution |
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