Applications of Dynamic Programming to Generalized Solutions for Hamilton — Jacobi Equations with State Constraints
Любовь Геннадьевна Шагалова · SOP Transactions on Applied Mathematics · 2014
Cauchy problem is considered for a Hamilton Jacobi equation with state constrains arising in molecular biology. This problem has no classical solution, and known concepts of generalized (minimax and/or viscosity) solution are not applicable to it. We introduce a new concept of a continuous generalized solution and propose a method for constructing this solution by solving an auxiliary optimal control problem.