PDE 11: Allen-Cahn equation
\[\frac{\partial u}{\partial t}=\varepsilon u_{xx} + u(1-u^2) \]
where \( u=u(x,t)\) is the solution.
Google: Allen-Cahn equation, bistable equation.
Challenges: non-linearity.
\[\frac{\partial u}{\partial t}=\varepsilon u_{xx} + u(1-u^2) \]
where \( u=u(x,t)\) is the solution.
Google: Allen-Cahn equation, bistable equation.
Challenges: non-linearity.