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Abstract Cauchy Problems: Three Approaches book cover

2nd Edition

Abstract Cauchy Problems Three Approaches

By Irina V. Melnikova, Alexei Filinkov Copyright 2027
296 Pages 1 B/W Illustrations
by Chapman & Hall

Although the theory of well-posed Cauchy problems is reasonably understood, ill-posed problems-involved in numerous mathematical models in physics, engineering, and finance can be approached in a variety of ways. The authors structured these approaches, identifying three main strategies for dealing with ill‑posed problems: semigroup methods, abstract distribution methods, and regularization... Read more

1. Semigroup Methods

2. Abstract Distribution Methods

3. Regularization Methods

4. Semigroup, Distribution, and Regularization Methods for Integro-Differential and Stochastic Problems

Biography

Irina V. Melnikova is a professor at the Ural Federal University, Ekaterinburg, Russia. She teaches both core mathematical courses and advanced specialised electives. Her research interests include ill-posed problems, generalized functions, operator semigroup theory, and stochastic analysis. She has over 150 research publications, including two monographs published by CHAPMAN & HALL/CRC.

Alexei Filinkov has a PhD in Mathematics (Differential Equations and Mathematical Physics) from the Ural State University, Russia. From 1995 to 2002 he undertook research and leadership roles in a variety of research projects at the University of Adelaide in the areas of risk analysis, financial modelling, ill-posed problems, stochastic analysis and generalised functions. From 2003 to 2024 he was a research scientist at the Defence Science and Technology Group (Australian Department of Defence) where he led projects focussed on risk-based approaches to defence and national security problems.

Currently he is an Honorary Principal Research Fellow at Torrens Resilience Initiative (Flinders University) and an Adjunct Senior Research Fellow at Adelaide University. Here, his research interests include investigation of risk and resilience paradigms for complex societal systems, and development of innovative mathematical tools for studying quantum phenomena.

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