Asia-Pacific Analysis and PDE Seminar

On March 21st, our Head Prof. Enrique Zuazua will talk on “Inverse design for conservation laws and Hamilton-Jacobi equations” at the Asia-Pacific Analysis and PDE Seminar organized by The University of Sydney.

Abstract. We discuss the problem of inverse design, or time inversion, for scalar conservation laws and Hamilton-Jacobi equations. The presence of singularities in the forward evolution is an obstruction for backward uniqueness and the unilateral bounds generated by the forward dynamics establishe thresholds on the set of reachable data. In this lecture we shall present our recent works in collaboration with Thibault Liard and Carlos Esteve, characterising the set of reachable states, identifying the multiplicity of initial data leading to a final target, and the determining the role of backward entropy or viscous solutions. We also develop numerical algorithms allowing to reconstruct the set of inversions and present some numerical experiments.

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Topics

The main focus of this seminar are recent research results of highest standard to the following research fields related to Analysis and PDEs:
• (Nonlinear) harmonic analysis with applications to PDEs
• Geometric Analysis
• Deterministic and stochastic Evolution equations
• Partial Differential Equations (PDEs)
In this weekly seminar series, talks from each community are intertwined, serving to highlight salient ideas, proofs and questions, and trigger new collaboration, which are important fertile ground for pushing forward research in Asia-Pacific region and world-wide.

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