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
Canonical name	SemilinearBiharmonicProblem1
Date of creation	2013-03-11 19:28:39
Last modified on	2013-03-11 19:28:39
Owner	linor (11198)
Last modified by	(0)
Numerical id	1
Author	linor (0)
Entry type	Definition