Journal of Mathematical Analysis and Applications· 2026Q1
A gradient flow for the porous medium equations with Dirichlet boundary conditions
- 1citations
- Q1SCImago
- 2026year
Short summary
A new gradient flow method constructs weak solutions for porous medium equations with Dirichlet boundary conditions using a modified Wasserstein distance.
AI-generated from the title and abstract; the full text is not read.
Key points
- Constructs weak solutions for porous medium equations with Dirichlet boundary conditions.
- Utilizes a minimizing movement scheme with an entropy functional and Wb2 distance.
- The Wb2 distance is a modified Wasserstein distance introduced by Figalli and Gigli (2010).
- Solutions are characterized as curves of maximal slope.
AI-generated from the title and abstract; the full text is not read.
Abstract
We consider the gradient flow structure of the porous medium equations with non-negative constant Dirichlet boundary conditions. We construct weak solutions to the equations via the minimizing movement scheme by considering an entropy functional with respect to W b 2 distance, which is a modified Wasserstein distance introduced by Figalli and Gigli (2010) [9] . Furthermore, the constructed solutions are characterized as curves of maximal slope in a suitable sense.
The authors' abstract, as published at the source. Journal of Mathematical Analysis and Applications, 2026 · DOI ↗
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Field: Applied Mathematics
Applied MathematicsMathematics