Incoming links: Neumann boundary condition
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.
Linear combination of a Dirichlet boundary condition and Neumann boundary condition at each point of the boundary.
Examples:
- heat equation when metal plaque is immersed in a large external environment of fixed temperature.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.Shown a solved example in the FreeFem tutorial: doc.freefem.org/tutorials/thermalConduction.html (github.com/FreeFem/FreeFem-doc/blob/1d5996d8b891fd553fd318321249c2c30f693fc3/source/tutorials/thermalConduction.rst)
Which boundary conditions lead to existence and uniqueness of a second order PDE Updated 2025-01-06 +Created 1970-01-01
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: