Overføringsligning

Overføringsligning is a term used in Danish and Norwegian to describe mathematical equations that model the transfer of a quantity within a system. They express how a property such as mass, energy, momentum, radiation, or information moves due to fluxes, sources and sinks, in accordance with conservation laws. In general, an overføringsligning links the rate of change of a quantity to its spatial transport and local generation or loss.

A common form is a conservation law in differential form: ∂u/∂t + ∇·F(u) = S(x,t,u), where u is the transported quantity, F its flux, and S a source term. Depending on the problem, F may depend linearly on u or include nonlinear effects. In one dimension and with a simple flux F(u) = v u, the equation reduces to ∂u/∂t + v ∂u/∂x = S. Variants cover many physical situations, such as heat conduction, advective transport, and diffusion of chemical species. Other instances include radiative transfer, Boltzmann transport, and models of population or traffic flow.

Solutions require initial conditions and boundary conditions, and can be obtained analytically for idealized cases or numerically for realistic systems (methods such as finite differences, finite volumes, and finite elements). The concept underpinning overføringsligninger is the universal idea of quantifying how quantities are transferred through space and time across disciplines.