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- W2951736173 abstract "Let begin{equation*} L=sum_{i,j=1}^da_{i,j}frac{partial^2}{partial x_ipartial x_j}-sum_{i=1}^db_ifrac{partial}{partial x_i} end{equation*} be a second order elliptic operator and consider the reaction-diffusion equation with Neumann boundary condition, begin{equation*} begin{aligned} L &nabla ucdot bar n=-h text{on} partial D; u namely, $u=h$ on $partial D$. The solutions to the above equations may possess a free boundary. When $D={|x| R:u(r)=0}$. We normalize the diffusion coefficient to be on unit order, consider the convection vector field to be on order $r^m$, $min R$, pointing either inward $(-)$ or outward $(+)$, and consider the reaction coefficient $Lambda$ to be on order $r^{-j}$, $jin R$. For both the Neumann boundary case and the Dirichlet boundary case, we show for which choices of $m$, $(pm)$ and $j$ a free boundary exists, and when it exists, we obtain its growth rate in $h$ as a function of $m$, $(pm)$ and $j$. These results are then used to study the free boundary in the non-radially symmetric case." @default.
- W2951736173 created "2019-06-27" @default.
- W2951736173 creator A5032276033 @default.
- W2951736173 date "2013-12-12" @default.
- W2951736173 modified "2023-09-27" @default.
- W2951736173 title "The Behavior of the Free Boundary for Reaction-Diffusion Equations with Convection in an Exterior Domain with Neumann or Dirichlet Boundary Condition" @default.
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- W2951736173 hasPublicationYear "2013" @default.
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