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Inverse problems with applications in science and engineering
1 online resource (xv, 342 pages) : illustrations
"Driven 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, Stokes), parabolic (heat, convection-reaction-diffusion) and hyperbolic (wave) Excellent reference for post-graduates and researchers in mathematics, engineering, and any other scientific disciplines that deal with inverse problems Contains both theory and numerical algorithms for solving all types of inverse and ill-posed problems"--
Introduction -- Inverse boundary-value problems -- Inverse initial-value problems -- Space-dependent heat sources -- Time-dependent heat sources -- Space- and time-dependent sources -- Inverse wave force problems -- Reconstruction of interfacial coefficients -- Identification of constant parameters in diffusion -- Time-dependent conductivity -- Space-dependent conductivity -- Nonlinear conductivity -- Anti-reflection coatings -- Flexural rigidity of a beam.
Daniel Lesnic, Leeds University, United Kingdom.
Includes bibliographical references and index.
Over 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, acoustics, with particular applications in the oil, nuclear and glass industries, medicine, corrosion engineering, river pollution, thermal barrier and anti-reflection coatings, etc. Currently, he is Associate Editor of the Journal of Inverse and Ill- Posed Problems, Inverse Problems in Science and Engineering and IMA Journal of Applied Mathematics, and he has published over 400 papers (http://www1.maths.leeds.ac.uk/applied/sta_.dir/lesnic/papers.html) in applied mathematics, edited 3 conference proceedings and he was Guest Editor of several journal issues on inverse problems. He is member of the London Mathematical Society (LMS) and the Eurasian Association for Inverse Problems. He has obtained several research grants and scholarships from the LMS, Engineering and Physical Sciences Research Council, Royal Society, British Council, Leverhulme Trust, the EU, and industry. He has successfully supervised 12 postdocs and 20 PhD students in inverse problems who have followed successful careers in both academia and industry. Currently, he supervises 2 PhD students. He was invited speaker at international conferences, e.g. the 3rd and 5th International Symposium on Inverse Problems, Design and Optimization, 2010, Joao Pessoa, Brazil and 2019, Tianjin, China; Inverse Problems and Applications, 2013, Linkoping, Sweden; the 12th and 13th International Conference on "Inverse and Ill-Posed Problems: Theory and Numerics", 2020 and 2021, Novosibirsk, Russia.
Inverse problems (Differential equations)
Problèmes inverses (Équations différentielles)
Boca Raton : Chapman & Hall/CRC Press, 2022