The Generalized Dock Problem

Details The Generalized Dock Problem The Generalized Dock Problem

2010-05-18

arxiv.org/abs/1005.3336v1

Mathematics

Analysis of PDEs

Scientific paper

We show existence and uniqueness for a linearized water wave problem in a two dimensional domain $G$ with corner, formed by two semi-axis $\Gamma_1$ and $\Gamma_2$ which intersect under an angle $\alpha\in (0,\pi ]$. The existence and uniqueness of the solution is proved by considering an auxiliary mixed problem with Dirichlet and Neumann boundary conditions. The latter guarantees the existence of the Dirichlet to Neumann map. The water wave boundary value problem is then shown to be equivalent to an equation like $v_{tt}+g\Lambda v=P$ with initial conditions, where $t$ stands for time, $g$ is the gravitational constant, $P$ means pressure, and $\Lambda$ is the Dirichlet to Neumann map. We then prove that $\Lambda$ is a positive self-adjoint operator.

Affiliated with

Also associated with

No associations

Rating

The Generalized Dock Problem does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Generalized Dock Problem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Generalized Dock Problem will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-477848