Smooth Solutions of a PDE with Nonsmooth Hamiltonian

Arik Melikyan
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Arik Melikyan: Institute for Problems in Mechanics, Russian Academy of Science

Chapter 6 in Generalized Characteristics of First Order PDEs, 1998, pp 199-225 from Springer

Abstract: Abstract Singular characteristics introduced in Chapter 2 and used for the solution of concrete problems in Chapters 2-5 are related to nonsmooth generalized (viscosity) solutions of nonlinear first order PDEs having smooth or nonsmooth Hamiltonians. In this chapter we will study the other source of singular characteristics associated with smooth (classical) solutions of a PDE. In such a problem, the singularities described by singular characteristics, are due to nonsmooth Hamiltonians, left hand side functions of PDEs. The simplest nonsmoothness of the Hamiltonians is considered which has one of the following characters: $$ F = \min \left[ {{F_0}{F_1}} \right],F = \max \left[ {{F_0}{F_1}} \right] $$

Keywords: Optimal Control Problem; Smooth Solution; Bellman Equation; Singular Surface; Singular Control (search for similar items in EconPapers)
Date: 1998
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DOI: 10.1007/978-1-4612-1758-9_7

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