Inverse design for conservation laws and Hamilton–Jacobi equations by E. Zuazua
Next Tuesday February 2nd, our Head Enrique Zuazua will be talking at One World PDE Seminars about: Inverse design for conservation laws and Hamilton–Jacobi equations
Zoom meeting link -provided 15min before talk!
We shall discuss the inverse problem, or inverse design problem, for a time-evolution Hamilton–Jacobi equation and the 1-d analog in the context of scalar conservation laws.
More precisely, given a target function and a time horizon, we aim to construct all the initial conditions for which the viscosity solution coincides the given target at the given time. As is common in this kind of nonlinear equation, the target might not be reachable. We first study the existence of at least one initial condition leading the system to the given target. The natural candidate, which in fact allows determining the reachability of the target, is the one obtained by reversing the direction of time in the equation. When is reachable, we construct the set of all the initial conditions for which the viscosity solutions lead to the final target.
We shall also discuss a number of open problems arising in this area and the possible link with other control problems through value functions, in particular in the context of reinforcement learning.
Speaker
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Enrique ZuazuaAlexander von Humboldt Professorship | Head of the Chair of Computational Mathematics | Professor of Applied MathematicsEnrique Zuazua (Eibar, Basque Country – Spain, 1961) holds an Alexander von Humboldt Professorship at the Friedrich–Alexander University (FAU), Erlangen (Germany). He is also the Director of the Chair of Computational Mathematics at Deusto Foundation, Universidad de Deusto (Bilbao, Basque Country-Spain) where he leads the research team funded by the ERC Advanced Grant DyCoN project. He is also a Professor of Applied Mathematics since 2001 at the Department of Mathematics of the Autonomous University of Madrid where he holds a Strategic Chair.
more about Enrique