A non-linear elliptic problem arising in petroleum engineering
Mayor de Montricher, Gilbert Franz
Tapia, Richard A.
Master of Arts
The problem of determining the temperature distribution of a body heated by radiation is formulated as a variational nonlinear partial differential equation. An existence and uniqueness theorem is proved for this problem. It is shown that Newton's method applied to this nonlinear problem gives a sequence of linear Dirichlet problems. Convergence results for Newton's method are also derived.