A nonlinear parabolic system arising from the eddy currents problem
The author considers a quasilinear parabolic system of second-order equations with ``quadratic gradient growth nonlinearity''. The problem under consideration is ``the mathematical formulation for the eddy currents problem''. This is when ``small pieces of metal are brought to the melting point with the Joule heating resulting from the eddy currents induced by an external variable magnetic field''. The main body of the paper consists of the existence, uniqueness and regularity results. Estimates of the solutions in different norms as well as some ``potential analysis'' enrich the material of the paper.
existence, uniqueness and regularity results
scientific article; zbMATH DE number 1513293