ABSTRACT

Driven by the advancement of industrial mathematics and the need for impact case studies, Inverse Problems with Applications in Science and Engineering thoroughly examines the state-of-the-art of some representative classes of inverse and ill-posed problems for partial differential equations (PDEs). The natural practical applications of this examination arise in heat transfer, electrostatics, porous media, acoustics, fluid and solid mechanics – all of which are addressed in this text.

Features:

  • Covers all types of PDEs — namely, elliptic (Laplace’s, Helmholtz, modified Helmholtz, biharmonic and Stokes), parabolic (heat, convection, reaction and diffusion) and hyperbolic (wave)
  • Excellent reference for post-graduates and researchers in mathematics, engineering and any other scientific discipline that deals with inverse problems
  • Contains both theory and numerical algorithms for solving all types of inverse and ill-posed problems

chapter Chapter 1|6 pages

Introduction

chapter Chapter 2|38 pages

Inverse Boundary-Value Problems

chapter Chapter 3|8 pages

Inverse Initial-Value Problems

chapter Chapter 4|18 pages

Space-Dependent Heat Sources

chapter Chapter 5|38 pages

Time-Dependent Heat Sources

chapter Chapter 6|24 pages

Space- and Time-Dependent Sources

chapter Chapter 7|38 pages

Inverse Wave Force Problems

chapter Chapter 8|12 pages

Reconstruction of Interfacial Coefficients

chapter Chapter 9|16 pages

Identification of Constant Parameters in Diffusion

chapter Chapter 10|24 pages

Time-Dependent Conductivity

chapter Chapter 11|20 pages

Space-Dependent Conductivity

chapter Chapter 12|18 pages

Nonlinear Conductivity

chapter Chapter 13|14 pages

Anti-Reflection Coatings

chapter Chapter 14|34 pages

Flexural Rigidity of a Beam