Doubly Nonlinear Diffusive PDEs: New Existence Results via Generalized Wasserstein Gradient Flows

Doubly Nonlinear Diffusive PDEs: New Existence Results via Generalized Wasserstein Gradient Flows

We prove an existence result for a large class of PDEs with a nonlinear Wasserstein gradient flow structure. We use the classical theory of Wasserstein gradient flow to derive an EDI formulation of our PDE and prove that under some integrability assumptions on the initial condition the PDE is satisf...

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Veröffentlicht in:SIAM journal on mathematical analysis 2024-12, Vol.56 (6), p.7043-7073
Hauptverfasser: Caillet, Thibault, Santambrogio, Filippo
Format: Artikel
Sprache:eng
Schlagworte:
Analysis of PDEs
Mathematics
Optimization and Control
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Zusammenfassung:We prove an existence result for a large class of PDEs with a nonlinear Wasserstein gradient flow structure. We use the classical theory of Wasserstein gradient flow to derive an EDI formulation of our PDE and prove that under some integrability assumptions on the initial condition the PDE is satisfied in the sense of distributions.
ISSN:0036-1410
1095-7154
DOI:10.1137/24M1639427