OPTIMIZING QUASI-DISSIPATIVE EVOLUTION EQUATIONS WITH THE MOMENT-SOS HIERARCHY

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F25%3A00383697" target="_blank" >RIV/68407700:21230/25:00383697 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.3934/dcds.2025051" target="_blank" >https://doi.org/10.3934/dcds.2025051</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3934/dcds.2025051" target="_blank" >10.3934/dcds.2025051</a>

Result language
angličtina
Original language name
OPTIMIZING QUASI-DISSIPATIVE EVOLUTION EQUATIONS WITH THE MOMENT-SOS HIERARCHY
Original language description
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 infinitedimensional moment-SOS hierarchy with global convergence guarantees. This covers in particular all reaction-diffusion equations with polynomial nonlinearity.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10102 - Applied mathematics

Project
<a href="/en/project/EH22_008%2F0004590" target="_blank" >EH22_008/0004590: Robotics and advanced industrial production</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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