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| Natura: | Preprint |
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2026
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| Accesso online: | https://arxiv.org/abs/2604.19389 |
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| _version_ | 1866914494958010368 |
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| author | Glogić, Irfan Kistner, Sarah Schörkhuber, Birgit |
| author_facet | Glogić, Irfan Kistner, Sarah Schörkhuber, Birgit |
| contents | We study the focusing semilinear heat equation with an additional defocusing Hénon-type nonlinearity, the coupling of which is measured by a constant $c >0$. For $c \in (0,c^*)$, the model admits a closed-form self-similar blowup solution in every space dimension $d \geq 1$. Restricting ourselves to the three-dimensional case, we study the stability of this solution under small non-radial perturbations. By working in intersection Sobolev spaces with additional angular regularity, we prove finite co-dimension stability for all admissible values of $c$. Furthermore, we analyze the spectrum of the underlying linearized operator and we prove stable blowup for the cubic-quintic case and $c$ sufficiently close to $c^*$. Finally, we discuss the situation for small values of $c$ and use a modified version of the classical GGMT criterion to give an upper bound on the number of unstable eigenvalues. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_19389 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Stable blowup profile for a semilinear Heat Equation with spatially inhomogeneous nonlinearity Glogić, Irfan Kistner, Sarah Schörkhuber, Birgit Analysis of PDEs We study the focusing semilinear heat equation with an additional defocusing Hénon-type nonlinearity, the coupling of which is measured by a constant $c >0$. For $c \in (0,c^*)$, the model admits a closed-form self-similar blowup solution in every space dimension $d \geq 1$. Restricting ourselves to the three-dimensional case, we study the stability of this solution under small non-radial perturbations. By working in intersection Sobolev spaces with additional angular regularity, we prove finite co-dimension stability for all admissible values of $c$. Furthermore, we analyze the spectrum of the underlying linearized operator and we prove stable blowup for the cubic-quintic case and $c$ sufficiently close to $c^*$. Finally, we discuss the situation for small values of $c$ and use a modified version of the classical GGMT criterion to give an upper bound on the number of unstable eigenvalues. |
| title | Stable blowup profile for a semilinear Heat Equation with spatially inhomogeneous nonlinearity |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2604.19389 |