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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2312.13284 |
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| _version_ | 1866913689493307392 |
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| author | Matthes, Daniel Rott, Eva-Maria Savaré, Giuseppe Schlichting, André |
| author_facet | Matthes, Daniel Rott, Eva-Maria Savaré, Giuseppe Schlichting, André |
| contents | We propose a spatial discretization of the fourth-order nonlinear DLSS equation on the circle. Our choice of discretization is motivated by a novel gradient flow formulation with respect to a metric that generalizes martingale transport. The discrete dynamics inherits this gradient flow structure, and in addition further properties, such as an alternative gradient flow formulation in the Wasserstein distance, contractivity in the Hellinger distance, and monotonicity of several Lypunov functionals. Our main result is the convergence in the limit of vanishing mesh size. The proof relies an a discrete version of a nonlinear functional inequality between integral expressions involving second order derivatives. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_13284 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A structure preserving discretization for the Derrida-Lebowitz-Speer-Spohn equation based on diffusive transport Matthes, Daniel Rott, Eva-Maria Savaré, Giuseppe Schlichting, André Analysis of PDEs Numerical Analysis We propose a spatial discretization of the fourth-order nonlinear DLSS equation on the circle. Our choice of discretization is motivated by a novel gradient flow formulation with respect to a metric that generalizes martingale transport. The discrete dynamics inherits this gradient flow structure, and in addition further properties, such as an alternative gradient flow formulation in the Wasserstein distance, contractivity in the Hellinger distance, and monotonicity of several Lypunov functionals. Our main result is the convergence in the limit of vanishing mesh size. The proof relies an a discrete version of a nonlinear functional inequality between integral expressions involving second order derivatives. |
| title | A structure preserving discretization for the Derrida-Lebowitz-Speer-Spohn equation based on diffusive transport |
| topic | Analysis of PDEs Numerical Analysis |
| url | https://arxiv.org/abs/2312.13284 |