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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2302.06363 |
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Table of Contents:
- We show that the parabolic equation $u_t + (-Δ)^s u = q(x) |u|^{α-1} u$ posed in a time-space cylinder $(0,T) \times \mathbb{R}^N$ and coupled with zero initial condition and zero nonlocal Dirichlet condition in $(0,T) \times (\mathbb{R}^N \setminus Ω)$, where $Ω$ is a bounded domain, has at least one nontrivial nonnegative finite energy solution provided $α\in (0,1)$ and the nonnegative bounded weight function $q$ is separated from zero on an open subset of $Ω$. This fact contrasts with the (super)linear case $α\geq 1$ in which the only bounded finite energy solution is identically zero.