Wavefront Solutions for Reaction-diffusion-convection Models with Accumulation Term and Aggregative Movements
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915152386850816 |
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| author | Cantarini, Marco Marcelli, Cristina Papalini, Francesca |
| author_facet | Cantarini, Marco Marcelli, Cristina Papalini, Francesca |
| contents | In this paper we analyze the wavefront solutions of parabolic partial differential equations of the type \[ g(u)u_τ+f(u)u_{x}=\left(D(u)u_{x}\right)_{x}+ρ(u),\quad u\left(τ,x\right)\in[0,1] \] where the reaction term $ρ$ is of monostable-type. We allow the diffusivity $D$ and the accumulation term $g$ to have a finite number of changes of sign.
We provide an existence result of travelling wave solutions (t.w.s.) together with an estimate of the threshold wave speed. Finally, we classify the t.w.s. between classical and sharp ones. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_10026 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Wavefront Solutions for Reaction-diffusion-convection Models with Accumulation Term and Aggregative Movements Cantarini, Marco Marcelli, Cristina Papalini, Francesca Analysis of PDEs Classical Analysis and ODEs 35K57, 35K65, 35C07, 35K55, 34B40, 34B16, 92D25 In this paper we analyze the wavefront solutions of parabolic partial differential equations of the type \[ g(u)u_τ+f(u)u_{x}=\left(D(u)u_{x}\right)_{x}+ρ(u),\quad u\left(τ,x\right)\in[0,1] \] where the reaction term $ρ$ is of monostable-type. We allow the diffusivity $D$ and the accumulation term $g$ to have a finite number of changes of sign. We provide an existence result of travelling wave solutions (t.w.s.) together with an estimate of the threshold wave speed. Finally, we classify the t.w.s. between classical and sharp ones. |
| title | Wavefront Solutions for Reaction-diffusion-convection Models with Accumulation Term and Aggregative Movements |
| topic | Analysis of PDEs Classical Analysis and ODEs 35K57, 35K65, 35C07, 35K55, 34B40, 34B16, 92D25 |
| url | https://arxiv.org/abs/2502.10026 |