The stochastic Klausmeier system and a stochastic Schauder-Tychonoff type theorem
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arXiv
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| Format: | Preprint |
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2019
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| _version_ | 1866911975357808640 |
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| author | Hausenblas, Erika Tölle, Jonas M. |
| author_facet | Hausenblas, Erika Tölle, Jonas M. |
| contents | On the one hand, we investigate the existence and pathwise uniqueness of a nonnegative martingale solution to the stochastic evolution system of nonlinear advection-diffusion equations proposed by Klausmeier with Gaussian multiplicative noise. On the other hand, we present and verify a general stochastic version of the Schauder-Tychonoff fixed point theorem, as its application is an essential step for showing existence of the solution to the stochastic Klausmeier system. The analysis of the system is based both on variational and semigroup techniques. We also discuss additional regularity properties of the solution. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1912_00996 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | The stochastic Klausmeier system and a stochastic Schauder-Tychonoff type theorem Hausenblas, Erika Tölle, Jonas M. Analysis of PDEs Functional Analysis Probability Primary 35K57, 60H15, Secondary 37N25, 47H10, 76S05, 92C15 On the one hand, we investigate the existence and pathwise uniqueness of a nonnegative martingale solution to the stochastic evolution system of nonlinear advection-diffusion equations proposed by Klausmeier with Gaussian multiplicative noise. On the other hand, we present and verify a general stochastic version of the Schauder-Tychonoff fixed point theorem, as its application is an essential step for showing existence of the solution to the stochastic Klausmeier system. The analysis of the system is based both on variational and semigroup techniques. We also discuss additional regularity properties of the solution. |
| title | The stochastic Klausmeier system and a stochastic Schauder-Tychonoff type theorem |
| topic | Analysis of PDEs Functional Analysis Probability Primary 35K57, 60H15, Secondary 37N25, 47H10, 76S05, 92C15 |
| url | https://arxiv.org/abs/1912.00996 |