A new transformation for the subcritical fast diffusion equation with source and applications
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915160248025088 |
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| author | Iagar, Razvan Gabriel Sánchez, Ariel |
| author_facet | Iagar, Razvan Gabriel Sánchez, Ariel |
| contents | A new transformation for radially symmetric solutions to the subcritical fast diffusion equation with spatially inhomogeneous source $$ \partial_tu=Δu^m+|x|^σu^p, $$ posed for $(x,t)\in\mathbb{R}^N\times(0,\infty)$ and with dimension and exponents $$ N\geq3, \quad 0<m<m_c:=\frac{N-2}{N}, \quad σ\in(-2,\infty), $$ is introduced. It plays a role of a kind of symmetry with respect to the critical exponents $$ m_s=\frac{N-2}{N+2}, \quad p_L(σ)=1+\frac{σ(1-m)}{2}, \quad p_s(σ)=\frac{m(N+2σ+2)}{N-2}. $$ This transformation is then applied for classifying self-similar solutions with or without finite time blow-up to the subcritical fast diffusion equation with source when $p>\max\{1,p_L(σ)\}$, having as starting point previous results by the authors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_13154 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A new transformation for the subcritical fast diffusion equation with source and applications Iagar, Razvan Gabriel Sánchez, Ariel Analysis of PDEs A new transformation for radially symmetric solutions to the subcritical fast diffusion equation with spatially inhomogeneous source $$ \partial_tu=Δu^m+|x|^σu^p, $$ posed for $(x,t)\in\mathbb{R}^N\times(0,\infty)$ and with dimension and exponents $$ N\geq3, \quad 0<m<m_c:=\frac{N-2}{N}, \quad σ\in(-2,\infty), $$ is introduced. It plays a role of a kind of symmetry with respect to the critical exponents $$ m_s=\frac{N-2}{N+2}, \quad p_L(σ)=1+\frac{σ(1-m)}{2}, \quad p_s(σ)=\frac{m(N+2σ+2)}{N-2}. $$ This transformation is then applied for classifying self-similar solutions with or without finite time blow-up to the subcritical fast diffusion equation with source when $p>\max\{1,p_L(σ)\}$, having as starting point previous results by the authors. |
| title | A new transformation for the subcritical fast diffusion equation with source and applications |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2502.13154 |