1,721,123 research outputs found
On the Singularities of the Viscosity Solutions to Hamilton-Jacobi-Bellman Equations
No full textCannarsa, Piermarco; Soner, H.M.. (1985). On the Singularities of the Viscosity Solutions to Hamilton-Jacobi-Bellman Equations. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/4076
Infinite dimensional Hamilton-Jacobi equations and Dirichlet boundary control problems of parabolic type
No full textCannarsa, Piermarco; Tessitore, Maria Elisabetta. (1994). Infinite dimensional Hamilton-Jacobi equations and Dirichlet boundary control problems of parabolic type. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/2575
Null controllability of semilinear weakly degenerate parabolic equations in bounded domains
No full textIn this paper we study controllability properties for semilinear degenerate parabolic equations with nonlinearities involving the first derivative in a bounded domain of R. Due to degeneracy, classical null controllability results do not hold in general. Thus we investigate results of 'regional null controllability', showing that we can drive the solution to rest at time T on a subset of the space domain, contained in the set where the equation is nondegenerate
Approximate controllability of degenerate parabolic equations governed by bilinear control arising in climatology
No full textNonlinear Optimal Control with Infinite Horizon for Distributed Parameter Systems and Stationary Hamilton–Jacobi Equations
Full text linkOptimal control problems, with no discount, are studied for systems governed by nonlinear 'parabolic' state equations, using a dynamic programming approach. If the dynamics are stabilizable with respect to cost, then the fact that the value function is a generalized viscosity solution of the associated Hamilton-Jacobi equation is proved. This yields the feedback formula. Moreover, uniqueness is obtained under suitable stability assumptions
Regional controllability of semilinear degenerate parabolic equations in bounded domains
No full textIn this paper we study controllability properties of semilinear degenerate parabolic equations. Due to degeneracy, classical null controllability results do not hold in general. Thus we investigate results of 'regional null controllability', showing that we can drive the solution to rest at time T on a subset of the space domain, contained in the set where the equation is nondegenerat
Carleman estimates for degenerate parabolic operators with applications to null controllability
No full textWe prove an estimate of Carleman type for the one dimensional heat equation
where is degenerate at . Such an estimate is derived for a special pseudo-convex weight function related to the degeneracy rate of . Then, we study the null controllability on of the semilinear degenerate parabolic equation
where is an element of subset of , and is locally Lipschitz with respect to
Compactness estimates for Hamilton-Jacobi equations depending on space
Full text linkWe study quantitative estimates of compactness in for the map , that associates to every given initial data u_0\in \Lip (\mathbb{R}^N) the corresponding solution of an Hamilton-Jacobi equation
with a convex and coercive Hamiltonian . We provide upper and lower bounds of order on the the Kolmogorov -entropy in of the image through the map of sets of bounded, compactly supported initial data. Quantitative estimates of compactness, as suggested by P.D. Lax, could provide a measure of the order of ``resolution'' and of
``complexity'' of a numerical method implemented for this equation. We establish these estimates deriving accurate a-priori bounds
on the Lipschitz, semiconcavity and semiconvexity constant of a viscosity solution when the initial data is semiconvex. The derivation of a small time controllability result for the above Hamilton-Jacobi equation is also fundamental to establish the lower bounds on the -entropy
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