Abstract Cauchy Problems by Irina V Melnikova
Relevant to a variety of mathematical models in physics, engineering and finance, this volume studies Cauchy problems that are not well-posed in the classical sense. It brings together and examines three major approaches to treating such problems: semigroup methods, abstract distribution methods, and regularization methods. Although developed over the last decade, this text provides a self-contained account of these methods and demonstrate the connections between them. Accessible to beginning graduate students, this volume brings together many different ideas to serve as a reference on modern methods for abstract linear evolution equations.-
Spectral Geometry of Partial Differential Operators
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Summable Spaces and Their Duals, Matrix Transformations and Geometric Properties
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Nonlinear Reaction-Diffusion-Convection Equations
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Symmetry and Quantum Mechanics
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Extending Structures
- Abstract Calculus
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Inequalities and Integral Operators in Function Spaces
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Finite Element Methods for Eigenvalue Problems
- Computation with Linear Algebraic Groups
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Monomial Algebras
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Introduction to the Potential Theory for the Time-Dependent Stokes System
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Differential Modules over Differential Rings
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Set Theoretical Aspects of Real Analysis
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Elastic Waves
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Lineability
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Spectral Methods Using Multivariate Polynomials On The Unit Ball
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Partial Differential Equations with Variable Exponents
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Localized Dynamics of Thin-Walled Shells
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Morrey Spaces
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Signal Processing
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Iterative Methods without Inversion
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Diagram Genus, Generators, and Applications
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Iterative Methods and Preconditioning for Large and Sparse Linear Systems with Applications
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Analysis on Function Spaces of Musielak-Orlicz Type
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Integration and Cubature Methods
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Separate and Joint Continuity
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Inverse Scattering Problems and Their Application to Nonlinear Integrable Equations
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Constructive Analysis of Semicircular Elements
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Spectral and Scattering Theory for Second Order Partial Differential Operators
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Modeling and Inverse Problems in the Presence of Uncertainty
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Dictionary of Inequalities
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Cremona Groups and the Icosahedron
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Markov Random Flights
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Willmore Energy and Willmore Conjecture
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Mathematical Modelling of Waves in Multi-Scale Structured Media
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Semigroups of Bounded Operators and Second-Order Elliptic and Parabolic Partial Differential Equations
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Tools for Infinite Dimensional Analysis
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Applications of Homogenization Theory to the Study of Mineralized Tissue
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Matrix Inequalities and Their Extensions to Lie Groups
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Calculus of Variations and Control Theory
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A Course on Malliavin-Skorohod Calculus for Additive Processes with Applications to Finance
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Beyond the Gibbs Paradigm
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Unbounded Operators and Subnormality
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Free Random Variables
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Non-Newtonian Sequence Spaces with Applications
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.
| SKU | Unavailable |
| ISBN 13 | 9781032894157 |
| ISBN 10 | 1032894156 |
| Title | Abstract Cauchy Problems |
| Author | Irina V Melnikova |
| Series | Chapman And Hall Crc Monographs And Research Notes In Mathematics |
| Condition | Unavailable |
| Binding Type | Hardback |
| Publisher | Chapman and Hall/CRC |
| Year published | 2026-08-12 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |