Shock wavefronts for parabolic equations with sign-changing diffusivity
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866915947556634624 |
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| author | Berti, Diego Corli, Andrea Malaguti, Luisa |
| author_facet | Berti, Diego Corli, Andrea Malaguti, Luisa |
| contents | We consider a reaction-diffusion equation in a one-dimensional space, where the diffusion coefficient changes sign from positive to negative and back to positive. The reaction term is bistable, with its interior zero located in the region where the diffusivity is negative. The model does not admit continuous wavefronts, i.e., continuous traveling waves that connect the steady states $0$ and $1$. We prove the existence of a family of shock wavefronts, that is, wavefronts with profiles exhibiting a jump discontinuity. We investigate the properties of these profiles and their propagation speeds. Finally, we apply the results to a recently proposed model describing the movement of a population composed of both isolated and grouped individuals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_19595 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Shock wavefronts for parabolic equations with sign-changing diffusivity Berti, Diego Corli, Andrea Malaguti, Luisa Analysis of PDEs 35K65, 35C07, 35K57, 92D25 We consider a reaction-diffusion equation in a one-dimensional space, where the diffusion coefficient changes sign from positive to negative and back to positive. The reaction term is bistable, with its interior zero located in the region where the diffusivity is negative. The model does not admit continuous wavefronts, i.e., continuous traveling waves that connect the steady states $0$ and $1$. We prove the existence of a family of shock wavefronts, that is, wavefronts with profiles exhibiting a jump discontinuity. We investigate the properties of these profiles and their propagation speeds. Finally, we apply the results to a recently proposed model describing the movement of a population composed of both isolated and grouped individuals. |
| title | Shock wavefronts for parabolic equations with sign-changing diffusivity |
| topic | Analysis of PDEs 35K65, 35C07, 35K57, 92D25 |
| url | https://arxiv.org/abs/2604.19595 |