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On the minimal time null controllability of the heat equation
A local min-orthogonal method for multiple solutions of strongly coupled elliptic systems
| 1. | Department of Mathematics, Texas A&M University, College Station, TX 77843, United States |
| 2. | Department of Mathematics, Texas A&M University, College Station, TX 77843-3368 |
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-$\Delta u=F_u(x;u,v),$ $x\in\Omega,
-$\Delta v=F_v(x;u,v),$ $x\in\Omega,
where $\Omega \subset \mathbb{R}^{N}$ ($N\ge 1$) is a bounded domain. A strongly coupled case where the potential $F(x;u,v)$ takes the form $|u|^{\alpha_1}|v|^{\alpha_2}$ with $\alpha_1, \alpha_2>1$ is specially studied. By using a local min-orthogonal method, both positive and sign-changing solutions are found and displayed.
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