Solvability of a doubly singular boundary value problem arising in front propagation for reaction-diffusion equations
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866929715425574912 |
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| author | Marcelli, Cristina |
| author_facet | Marcelli, Cristina |
| contents | The paper deals with the solvability of the following doubly singular boundary value problem \[\begin{cases} \dot z = c g(u)-f(u) -\dfrac{h(u)}{z^α}\\ z(0^+)=0, z(1^-)=0, \ z(u)>0 \text{ in } (0,1)\end{cases}\] naturally arising in the study of the existence and properties of travelling waves for reaction-diffusion-convection equations governed by the $p-$Laplacian operator.
Here $c,α$ are real parameters, with $α>0$, and $f,g,h$ are continuous functions in $[0,1]$, with \[ h(0)=h(1), \quad h(u)>0 \text{ in } (0,1).\] |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_10035 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Solvability of a doubly singular boundary value problem arising in front propagation for reaction-diffusion equations Marcelli, Cristina Analysis of PDEs Classical Analysis and ODEs 34B15, 34B16, 34B08, 35C07, 35K57 The paper deals with the solvability of the following doubly singular boundary value problem \[\begin{cases} \dot z = c g(u)-f(u) -\dfrac{h(u)}{z^α}\\ z(0^+)=0, z(1^-)=0, \ z(u)>0 \text{ in } (0,1)\end{cases}\] naturally arising in the study of the existence and properties of travelling waves for reaction-diffusion-convection equations governed by the $p-$Laplacian operator. Here $c,α$ are real parameters, with $α>0$, and $f,g,h$ are continuous functions in $[0,1]$, with \[ h(0)=h(1), \quad h(u)>0 \text{ in } (0,1).\] |
| title | Solvability of a doubly singular boundary value problem arising in front propagation for reaction-diffusion equations |
| topic | Analysis of PDEs Classical Analysis and ODEs 34B15, 34B16, 34B08, 35C07, 35K57 |
| url | https://arxiv.org/abs/2502.10035 |