A01=Alexei Filinkov
A01=Irina V. Melnikova
Abstract Cauchy Problems
Author_Alexei Filinkov
Author_Irina V. Melnikova
banach
Banach Space
Category=PBKJ
Cauchy
Cauchy Dirichlet Problem
Cauchy Problem
Cauchy Sequence
Classical Sobolev Spaces
Correctness Class
Dense
dirichlet
Dirichlet Problem
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
error
Error Estimates
estimate
functional analysis
Heat Equation
Ill Posed Problems
ill-posed problem solution methods
Integrated Semigroup
Inverse Cauchy Problem
linear evolution equations
Linear Operator
mathematical modeling
method
methods
operator theory
parameter
partial differential equations
Quasi-reversibility Method
regularization
Regularization Methods
Regularization Parameter
Residual Method
Rst Kind
semigroup
Semigroup Method
Sin Kx
space
Unbounded Linear Operator
Unbounded Operator
Unique Generalized Solution
weak solutions
Product details
- ISBN 9781584882503
- Weight: 650g
- Dimensions: 156 x 234mm
- Publication Date: 27 Mar 2001
- Publisher: Taylor & Francis Inc
- Publication City/Country: US
- Product Form: Hardback
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Although the theory of well-posed Cauchy problems is reasonably understood, ill-posed problems-involved in a numerous mathematical models in physics, engineering, and finance- can be approached in a variety of ways. Historically, there have been three major strategies for dealing with such problems: semigroup, abstract distribution, and regularization methods. Semigroup and distribution methods restore well-posedness, in a modern weak sense. Regularization methods provide approximate solutions to ill-posed problems. Although these approaches were extensively developed over the last decades by many researchers, nowhere could one find a comprehensive treatment of all three approaches.
Abstract Cauchy Problems: Three Approaches provides an innovative, self-contained account of these methods and, furthermore, demonstrates and studies some of the profound connections between them. The authors discuss the application of different methods not only to the Cauchy problem that is not well-posed in the classical sense, but also to important generalizations: the Cauchy problem for inclusion and the Cauchy problem for second order equations.
Accessible to nonspecialists and beginning graduate students, this volume brings together many different ideas to serve as a reference on modern methods for abstract linear evolution equations.
Melnikova, Irina V.; Filinkov, Alexei
