A nonlinear parabolic system arising from the eddy currents problem (Q1582395)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: A nonlinear parabolic system arising from the eddy currents problem |
scientific article; zbMATH DE number 1513293
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A nonlinear parabolic system arising from the eddy currents problem |
scientific article; zbMATH DE number 1513293 |
Statements
A nonlinear parabolic system arising from the eddy currents problem (English)
0 references
3 October 2000
0 references
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.
0 references
\(L^{1,\gamma}\) estimate
0 references
quadratic gradient growth
0 references
existence, uniqueness and regularity results
0 references
