Seminar on Qualitative Theory of Differential Equations - Philippe Souplet (29.4.2026)

Thursday 30.4.2026 at 14:00, Lecture room M 223

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 Philippe Souplet (Université Sorbonne Paris Nord):
Classification of entire and ancient solutions of the diffusive Hamilton-Jacobi equation

Abstract:
We study the Liouville type classification and symmetry properties, in Rⁿ and in a half-space with Dirichlet boundary conditions, for entire and ancient solutions of the diffusive Hamilton-Jacobi equation, which arises in optimal stochastic control, in KPZ type models of surface growth and in studies of gradient blow-up. In particular we obtain the optimal Liouville type theorem for ancient solutions in Rⁿ and we completely classify entire solutions in a half-space. The proofs rely on new and optimal, local estimates of Bernstein and Li-Yau type, combined with integral estimates, a translation-compactness procedure and comparison arguments.

This is a joint work with Loth Chabi.

 

 

 

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