Conservation Law

A local balance statement that the time change of an extensive quantity within a region equals the net flux across the region boundary plus any internal source or sink; it constrains admissible dynamics by enforcing local invariance properties.

A partial differential equation expressing the local balance of a conserved quantity, typically written in differential form as time derivative of a density plus the divergence of its flux equals zero (or a source term), ensuring the quantity changes only by transport and sources/sinks.