Derivation of the fourth-order DLSS equation with nonlinear mobility via chemical reactions
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912636216541184 |
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| author | Mielke, Alexander Schlichting, André Stephan, Artur |
| author_facet | Mielke, Alexander Schlichting, André Stephan, Artur |
| contents | We provide a derivation of the fourth-order DLSS equation based on an interpretation as a chemical reaction network. We consider the rate equation on the discretized circle for a process in which pairs of particles occupying the same site simultaneously jump to the two neighboring sites; the reverse process involves pairs of particles at adjacent sites simultaneously jumping back to the site located between them. Depending on the rates, in the vanishing-mesh-size limit we obtain either the classical DLSS equation or a variant with nonlinear mobility of power type. Via EDP convergence, we identify the limiting gradient structure to be driven by entropy with respect to a generalization of diffusive transport with nonlinear mobility. Interestingly, the DLSS equation with power-type mobility shares qualitative similarities with the fast diffusion and porous medium equation, since we find traveling wave solutions with algebraic tails or compactly supported polynomials, respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_07149 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Derivation of the fourth-order DLSS equation with nonlinear mobility via chemical reactions Mielke, Alexander Schlichting, André Stephan, Artur Analysis of PDEs Numerical Analysis Mathematical Physics 35A15, 35K55, 35A35, 47J35, 65M08 We provide a derivation of the fourth-order DLSS equation based on an interpretation as a chemical reaction network. We consider the rate equation on the discretized circle for a process in which pairs of particles occupying the same site simultaneously jump to the two neighboring sites; the reverse process involves pairs of particles at adjacent sites simultaneously jumping back to the site located between them. Depending on the rates, in the vanishing-mesh-size limit we obtain either the classical DLSS equation or a variant with nonlinear mobility of power type. Via EDP convergence, we identify the limiting gradient structure to be driven by entropy with respect to a generalization of diffusive transport with nonlinear mobility. Interestingly, the DLSS equation with power-type mobility shares qualitative similarities with the fast diffusion and porous medium equation, since we find traveling wave solutions with algebraic tails or compactly supported polynomials, respectively. |
| title | Derivation of the fourth-order DLSS equation with nonlinear mobility via chemical reactions |
| topic | Analysis of PDEs Numerical Analysis Mathematical Physics 35A15, 35K55, 35A35, 47J35, 65M08 |
| url | https://arxiv.org/abs/2510.07149 |