Incoming links: Neumann boundary condition
Cauchy boundary condition Updated 2025-07-16
Sets both a Dirichlet boundary condition and a Neumann boundary condition for a single part of the boundary.
Can be used for hyperbolic partial differential equations.
We understand intuitively that this imposes stricter requirements on solutions, which makes it easier to guarantee uniqueness, but also harder to have existence. TODO intuitively why hyperbolic need this extra level of restriction.
Robin boundary condition Updated 2025-07-16
Linear combination of a Dirichlet boundary condition and Neumann boundary condition at each point of the boundary.
Examples:
- In this case, the normal derivative at the boundary is proportional to the difference between the temperature of the boundary and the fixed temperature of the external environment.The result as time tends to infinity is that the temperature of the plaque tends to that of the environment.
www.cns.gatech.edu/~predrag/courses/PHYS-6124-12/StGoChap6.pdf 6.1 "Classification of PDE's" clarifies which boundary conditions are needed for existence and uniqueness of each type of second order of PDE: