Daniel Lesnic

Inverse Problems with Applications in Science and Engineering (eBook, ePUB)

• Format: ePub

Produktbeschreibung

Driven the advancement of industrial mathematics and the need for impact case studies, this book thoroughly examines the state-of-the-art of some representative classes of inverse and ill-posed problems for partial differential equations (PDEs).

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Produktdetails

• Verlag: Taylor & Francis
• Seitenzahl: 358
• Erscheinungstermin: 9. November 2021
• Englisch
• ISBN-13: 9780429683244
• Artikelnr.: 62613158

Autorenporträt

For the past 30 years, Daniel Lesnic (PhD 1995, Leeds University, Professor in Applied Mathematics since 2008) has worked on a diverse range of industrial and environmental mathematical inverse problems which have involved close and lasting contact with various scientists, engineers and experimentalists, both nationally and internationally. Topics include heat and mass transfer, porous media, rock mechanics, elasticity, fluid flow, bio-heat conduction, mechanics of aerosols and acoustics, with particular applications in the oil, nuclear and glass industries, medicine, corrosion engineering, river pollution, thermal barriers and anti-reflective coatings. Professor Lesnic is the Associate Editor of the Journal of Inverse and Ill-Posed Problems, Inverse Problems in Science and Engineering and the IMA Journal of Applied Mathematics and has published over 400 papers (http://www1.maths.leeds.ac.uk/applied/staff.dir/lesnic/papers.html) in applied mathematics, edited three conference proceedings and was the Guest Editor of several journal issues on inverse problems. He is also a member of the London Mathematical Society (LMS) and the Eurasian Association for Inverse Problems.

Inhaltsangabe

1. Introduction. 1.1. Classification of inverse problems. 1.2. Systems of
linear algebraic equations. 1.3. Regularization methods. 2. Inverse
boundary-value problems. 2.1 Cauchy problem for the Laplace equation. 2.2.
Cauchy problem for the Stokes system. 2.3. Cauchy-type problems for the
biharmonic equation. 2.4. Cauchy problems for the heat equation. 2.5.
Conclusions. 3. Inverse initial-value problems. 3.1. Quasi-reversibility
methods. 3.2. Logarithmic convexity methods. 3.3. Non-local initial-value
methods. 4. Space-dependent heat sources. 4.1. Space-dependent heat source
identification. 4.2. Simultaneous identification of the space-dependent
heat source and initial temperature. 5. Time-dependent heat sources. 5.1.
Time-dependent heat source identification. 5.2. Non-local variants. 6.
Space- and time-dependent sources. 6.1. Additive space- and time-dependent
heat sources. 6.2. Additive space- and time-dependent heat sources.
Integral observations. 6.3. Multiplicative space- and time-dependent
source. 7. Inverse wave force problems. 7.1. Determination of a
space-dependent force in the one-dimensional wave equation from Cauchy
data. 7.2. Determination of the force function in the multi-dimensional
wave equation from Cauchy data. 7.3. Determination of a space-dependent
force function from final or time-averaged displacement data. 8.
Reconstruction of interfacial coefficients. 8.1. Introduction. 8.2.
Mathematical formulation. 8.3. Conjugate gradient method (CGM). 8.4.
Numerical results and discussions. 9. Identification of constant parameters
in diffusion. 9.1. Homogeneous and isotropic diffusion. 9.2. A
two-dimensional tracer dispersion problem. 9.3. Determination of constant
thermal properties. 10. Time-dependent conductivity. 10.1. Identification
of the time-dependent conductivity. 10.2. Identification of the
time-dependent conductivity of an inhomogeneous diffusive material. 10.3.
Finding the time-dependent diffusion coefficient from an integral
observation. 11. Space-dependent conductivity. 11.1. Reconstruction of a
permeability function from core measurements and pressure data. 11.2.
Discontinuous anisotropic conductivity. 11.3. Reconstruction of an
orthotropic conductivity. 12. Nonlinear conductivity. 12.1. Determination
of nonlinear thermal properties. 12.2. Nonlinear and heterogeneous
conductivity. 13. Anti-reflection coatings. 13.1. Mathematical model and
analysis. 13.2. Numerical implementation. 13.3. Conclusions. 14. Flexural
rigidity of a beam. 14.1. Distributed parameters in beam-type systems.
14.2. The comparison model method. 14.3. Determination of the flexural
rigidity of a beam from limited boundary measurements.