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| Title: | A Newton-Imbedding Procedure for Solutions of Semilinear Boundary Value Problems in Sobolev Spaces |
| Authors: | Hsiao, G.C. |
| Keywords: | nonlinear problem
Newton-imbedding iteration
variational formulation
boundary integral equations
a priori estimate |
| Issue Date: | 12-Jul-2006 |
| Series/Report no.: | Technical Report;2006-05 |
| Abstract: | This paper is concerned with the application of the Newton-imbedding
iteration procedure to nonlinear boundary value problems in Sobolev
spaces. A simple model problem for the second-order semilinear elliptic
equations is considered to illustrate the main idea. The essence
of the method hinges on the a priori estimates of solutions of the associated
linear problem in appropriate Sobolev spaces. It is to our
surprise that H1(Ω)-solution is not smooth enough to guarantee the
convergence of the sequence generated by the procedure. Existence
and uniqueness of solution to the original nonlinear problem are established
constructively. An application of this approach to the Lamé
system with nonlinear body force and its generalization to contain a
nonlinear surface traction in elasticity will also be discussed. |
| URI: | http://dspace.udel.edu:8080/dspace/handle/19716/2453 |
| Appears in Collections: | Math Technical Report Series
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