The construction of a continuous generalized solution for the Hamilton-Jacobi equations with state constraints
We consider a boundary value problem with state constraints for a nonlinear non-coercive Hamilton-Jacobi equation. We introduce a new definition of continuous generalized solution of the problem and apply this definition to nonlinear non-coercive equation arising in molecular biology. The construction for generalized solution with additional requirements to structure is provided for this equation. Connections with viscosity generalized solutions are discussed. Results of computer simulations are exposed.