A supersolution approach to doubly degenerate parabolic equations with weights
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918261192392704 |
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| author | Andreucci, Daniele Tedeev, Anatoli F. |
| author_facet | Andreucci, Daniele Tedeev, Anatoli F. |
| contents | We consider the Cauchy problem in the Euclidean space for a doubly
degenerate parabolic equation with a space-dependent exponential
weight, where the exponent satisfies the doubling condition. In
particular, both the so called logconvex and logconcave cases may be
considered. Under the additional natural assumptions we construct
supersolutions and subsolutions allowing us to control the precise
sharp temporal decay bounds. We apply our results also to an
equation with inhomogeneous density, via a suitable variable
transformation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_20373 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A supersolution approach to doubly degenerate parabolic equations with weights Andreucci, Daniele Tedeev, Anatoli F. Analysis of PDEs 35K55 35K65 35B40 We consider the Cauchy problem in the Euclidean space for a doubly degenerate parabolic equation with a space-dependent exponential weight, where the exponent satisfies the doubling condition. In particular, both the so called logconvex and logconcave cases may be considered. Under the additional natural assumptions we construct supersolutions and subsolutions allowing us to control the precise sharp temporal decay bounds. We apply our results also to an equation with inhomogeneous density, via a suitable variable transformation. |
| title | A supersolution approach to doubly degenerate parabolic equations with weights |
| topic | Analysis of PDEs 35K55 35K65 35B40 |
| url | https://arxiv.org/abs/2512.20373 |