The semiflow of a reaction diffusion equation with a singular potential
| dc.creator | Karachalios, Nikos I. | |
| dc.creator | Zographopoulos, Nikos B. | |
| dc.date | 2008-02-13 | |
| dc.date.accessioned | 2026-07-07T09:20:29Z | |
| dc.date.available | 2026-07-07T09:20:29Z | |
| dc.description | We study the semiflow $\mathcal{S}(t)$ defined by a semilinear parabolic equation with a singular square potential $V(x)=\fracμ{|x|^2}$. It is known that the Hardy-Poincaré inequality and its improved versions, have a prominent role on the definition of the natural phase space. Our study concerns the case $0<μ\leqμ^*$, where $μ^*$ is the optimal constant for the Hardy-Poincaré inequality. On a bounded domain of $\mathbb{R}^N$, we justify the global bifurcation of nontrivial equilibrium solutions for a reaction term $f(s)=λs-|s|^{2γ}s$, with $λ$ as a bifurcation parameter. The global bifurcation result is used to show that any solution $ϕ(t)=\mathcal{S}(t)ϕ_0$, initiating form initial data $ϕ_0\geq 0$ ($ϕ_0\leq 0$), $ϕ_0\not\equiv 0$, tends to the unique nonnegative (nonpositive) equilibrium. | |
| dc.description | 20 pages, 3 figures | |
| dc.identifier | https://arxiv.org/abs/0802.1804 | |
| dc.identifier | http://arxiv.org/abs/0802.1804 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/154737 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Dynamical Systems | |
| dc.subject | 35K57, 35B40, 35B41, 37L30 | |
| dc.title | The semiflow of a reaction diffusion equation with a singular potential | |
| dc.type | text |