Year: 2025
Type: article
Abstract: We prove that there is no relaxation gap between a quasi-dissipative nonlinear evolution equation in a Hilbert space and its linear Liouville equation reformulation on probability measures. In other words, strong and generalized solutions of such equations are unique in the class of measure-valued solutions. As a major consequence, non-convex numerical optimization over these non-linear partial differential equations can be carried out with the infinite-dimensional moment-SOS hierarchy with global convergence guarantees. This covers in particular all reaction-diffusion equations with polynomial nonlinearity.
DOI: 10.3934/dcds.2025051
Institutions: Centre National de la Recherche Scientifique, Laboratoire d'Analyse et d'Architecture des Systèmes, Université de Toulouse, École Centrale de Nantes, Laboratoire des Sciences du Numérique de Nantes, Nantes Université, Institut national de recherche en sciences et technologies du numérique, Université de Montpellier, Institut Montpelliérain Alexander Grothendieck
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4409436262