## Hyperbolic Functional Differential Inequalities and ApplicationsThis book is intended as a self-contained exposition of hyperbolic functional dif ferential inequalities and their applications. Its aim is to give a systematic and unified presentation of recent developments of the following problems: (i) functional differential inequalities generated by initial and mixed problems, (ii) existence theory of local and global solutions, (iii) functional integral equations generated by hyperbolic equations, (iv) numerical method of lines for hyperbolic problems, (v) difference methods for initial and initial-boundary value problems. Beside classical solutions, the following classes of weak solutions are treated: Ca ratheodory solutions for quasilinear equations, entropy solutions and viscosity so lutions for nonlinear problems and solutions in the Friedrichs sense for almost linear equations. The theory of difference and differential difference equations ge nerated by original problems is discussed and its applications to the constructions of numerical methods for functional differential problems are presented. The monograph is intended for different groups of scientists. Pure mathemati cians and graduate students will find an advanced theory of functional differential problems. Applied mathematicians and research engineers will find numerical al gorithms for many hyperbolic problems. The classical theory of partial differential inequalities has been described exten sively in the monographs [138, 140, 195, 225). As is well known, they found applica tions in differential problems. The basic examples of such questions are: estimates of solutions of partial equations, estimates of the domain of the existence of solu tions, criteria of uniqueness and estimates of the error of approximate solutions. |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

Initial Problems on the Haar Pyramid | 1 |

Existence of Solutions on the Haar Pyramid | 41 |

Numerical Methods for Initial Problems | 69 |

Copyright | |

7 other sections not shown

### Other editions - View all

Hyperbolic Functional Differential Inequalities and Applications Z. Kamont No preview available - 2012 |

### Common terms and phrases

assume assumptions of Theorem Banach space bicharacteristics Caratheodory solutions Cauchy problem Chaplygin classical solutions completes the proof consider the Cauchy continuous function convergence defined denote derivatives difference equation difference methods differential functional equations Dxu(x,y Eo.h U Eh equicontinuous exactly one solution existence and uniqueness existence of solutions exists a function follows from Assumption follows from Theorem function f functional differential equations functional differential inequalities functional differential problems functional variable given functions hyperbolic functional initial condition initial problems JH(x Kamont Lemma linear Lipschitz condition Math method of lines mixed problem nondecreasing with respect nonlinear obtain operator partial differential equations Polon quasilinear Remark ro,a satisfies Assumption satisfies the conditions satisfies the Lipschitz satisfies the Volterra sequence solution of problem Suppose that Assumption supremum norm uniformly convergent unique solution viscosity solutions Volterra condition x Rn