Conservation laws for heat equation on curved surfaces

The conservation laws for a (1+n)(1+n)-dimensional heat equation on curved surfaces are constructed by using a partial Noether’s approach associated with the partial Lagrangian. The partial Noether determining equation for the general case n≥2n≥2 gives some extra conditions on gauge terms and conserved vectors. The analysis is then applied for heat equations on cone, sphere, torus and plane. Moreover, we use the symmetry conservation law relation and some new conservation laws are deduced.