Forward and Inverse Problems: An Exploration of Differential Equations

Senior Thesis

Abstract

This thesis has two parts. The first discusses the Laplacian and how to solve it in arbitrary domains. It will cover Dirichlet’s Principle, the Fundamental Solution, and Green’s Function, as well as examples on the half space and ball. The second will cover the inverse problem of detecting corrosion in a plate of metal using heat. It will discuss the general solution method, regularization of the solution, and analyze the results.

Attributes

Attribute NameValues
Created by
  • mcharnle

Contributor
  • Matthew Charnley

  • Advisor: Nancy Stanton

Subject
  • Mathematics

Bibliographic Citation
  • Undergraduate Thesis, University of Notre Dame, April 2013

Language
  • English

Source
  • THESIS_FINAL.tex

Publisher
  • University of Notre Dame

Record Visibility Public

Digital Object Identifier

doi:10.7274/R0PN93H4

This DOI is the best way to cite this senior thesis.

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