Semilinear biharmonic problem

A semilinear biharmonic problem with so-called Navier boundary conditions is

\begin{displaymath} (BH) \;\; \left \{ \begin{array}{ll} \Delta^2 v= f(x, v) &... ... v=\Delta v=0 &\, x\in \partial \Omega \end{array} \right. \end{displaymath}

where $\Omega\subset {\mathbb{R}}^N (N\ge 1)$ is an open bounded domain, $f(x, v)\in \mathcal{C}^{1}(\overline{\Omega} \times \mathbb{R}; \mathbb{R})$ in $v \in \mathbb{R}$.
Numerical results for the case $\Omega = (-2,2)\times (-2,2) $ and $f(x,v)=v^p$: p=0.1, 0.7, 1.3, 7.
Note that $u=-\Delta v$.



Created by X. Chen

Nov-30-2007