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Pattern formation in reaction-diffusion systems with $D_2$-symmetric kinetics
Multiplicity and stability result for semilinear parabolic equations
| 1. | Department of Mathematics, Yokohama National University, 156 Tokiwadai Hodogaya-ku - Yokohama |
| 2. | Department of Mathematics, Dong-A University, Handan-2Dong, Saha-ku, Pusan, South Korea |
$\qquad\qquad \frac{\partial u}{\partial t}-\Delta_x u -\lambda_1 u +g(u) =s \phi + h$ in $ R\times \Omega$
$\qquad\qquad u(t,x) =0 $ on $R\times \partial \Omega$
$\qquad\qquad u(0,x)=u(2\pi, x)$ on $\Omega$
where $g$ is a continuous function on $R$, $\phi$ denotes the positve normalized eigenfunction corresponding to the first eigenvalue $\lambda_1$ of problem (L), $s \in R$, and $h \in C([0,2\pi],C^1_0(\overline{\Omega})).$
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