Given the viscosity solution, u, of the Cauchy problem ut + (f(t,x),∇u)+r|A(t,x)∇u| = 0 in ]0,T[× ℝn with u(0,x) = g(x), we describe the arc structure of the set of the points of non-differentiability for u. Moreover, we give a result on the propagation of singularities along the generalized characteristics.
Albano P. (2002). On the singular set for solutions to a class of Hamilton-Jacobi-Bellman equations. NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 9(4), 473-497 [10.1007/PL00012610].
On the singular set for solutions to a class of Hamilton-Jacobi-Bellman equations
Albano P.
2002
Abstract
Given the viscosity solution, u, of the Cauchy problem ut + (f(t,x),∇u)+r|A(t,x)∇u| = 0 in ]0,T[× ℝn with u(0,x) = g(x), we describe the arc structure of the set of the points of non-differentiability for u. Moreover, we give a result on the propagation of singularities along the generalized characteristics.File in questo prodotto:
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