PDE 23: Eikonal equation

\[ |\nabla \phi(\mathbf{x})| = \frac{1}{c(\mathbf{x})}, \] where \(|\cdot|\) is the Euclidean norm and \(c(\mathbf{x})>0\) is the propagation speed at \( \mathbf{x} \in \mathbb{R}^d.\) Consider Dirichlet boundary conditions \(\phi(\mathbf{x})|_{\partial\Omega} = 0.\)

What is the solution if you consider the special case \(c(\mathbf{x})=1\)?

Google-åte: Eikonal equation, wave propagation, signed distance