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Hyperbolic Functional Differential Inequalities and Applications (Mathematics and Its Applications (closed))
Rok: 1999
ISBN: 9780792357919
OKCZID: 110109175
Citace (dle ČSN ISO 690):
KAMONT, Zdzislaw. Hyperbolic functional differential inequalities and applications. Dordrecht: Kluwer Academic Publishers, 1999. xiii, 304 p. Mathematics and Its Applications, vol. 486.
Anotace
This monograph is a self-contained exposition of hyperbolic functional differential inequalities and their applications, on which topic the present author initiated research. It aims to give a systematic and unified presentation of recent developments in the following problems: functional differential inequalities generated by initial and mixed problems; existence theory of local and global solutions; functional integral equations generated by hyperbolic equations; numerical methods of lines for hyperbolic problems; and difference methods for initial and initial-boundary value problems. Besides classical solutions, some classes of weak solutions are also treated, such as Caratheodory solutions for quasilinear equations, entropy solutions and viscosity solutions for nonlinear problems, and solutions in the Friedrichs sense for almost linear equations. The theory of difference and differential difference equations generated by original problems and its applications to the construction of numerical methods for functional differential problems is also discussed. Audience: This volume will be valuable to pure mathematicians and graduate students whose work involves the theory of functional differential problems at an advanced level. Applied mathematicians and research engineers will find the numerical algorithms for many hyperbolic problems of interest.