# Semilinear biharmonic problem

Semilinear biharmonic problem

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

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

where $\Omega\subset{\mathbb{R}}^{N}(N\geq 1)$ 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 $u=-\Delta v$.

Title Semilinear biharmonic problem SemilinearBiharmonicProblem1 2013-03-11 19:28:39 2013-03-11 19:28:39 linor (11198) (0) 1 linor (0) Definition