📂Partial Differential Equations

Robin Boundary Conditions

Definition¹

Let’s assume that a partial differential equation is defined in an open set $\Omega$. The following boundary conditions are called Robin boundary conditions.

$$u + \dfrac{\partial u}{\partial \nu} = 0 \quad \text{on }\partial \Omega$$

Here, $\nu$ represents the outward unit normal vector.

Description

Example

For instance, solving the Poisson’s equation with given Robin boundary conditions is to find $u$ that satisfies the following.

$$\left\{ \begin{align*} -\Delta u = f & \quad \text{in } \Omega \\ u + \dfrac{\partial u}{\partial \nu} = 0 & \quad \text{on }\partial \Omega \end{align*} \right.$$

See Also

• Boundary value problem
• Dirichlet boundary condition
• Neumann boundary condition