Tapia, Richard A.2016-04-222016-04-221971Mayor de Montricher, Gilbert Franz. "A non-linear elliptic problem arising in petroleum engineering." (1971) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/89973">https://hdl.handle.net/1911/89973</a>.https://hdl.handle.net/1911/89973The 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.42 ppengCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.ThesisRICE1008reformatted digitalThesis Math. Sci. 1971 Mayor de Montr