Some Existence Theorems for Semilinear Hyperbolic Systems in One Space Variable PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Some Existence Theorems for Semilinear Hyperbolic Systems in One Space Variable PDF full book. Access full book title Some Existence Theorems for Semilinear Hyperbolic Systems in One Space Variable by Luc C. Tartar. Download full books in PDF and EPUB format.
Author: Luc C. Tartar
Publisher:
ISBN:
Category : Differential equations, Hyperbolic
Languages : en
Pages : 32
Get Book Here
Book Description
We study semilinear hyperbolic systems with quadratic nonlinearities which originate in the kinetic theory of gas as a simplification of Boltzmann's equation. Local existence is well known for these equations and the main problem is to prove global existence for nonnegative bounded data. Except for the unrealistic case where a bounded invariant region exists, no result of this type is known in three space dimensions. As in all preceding results, based on the work of Mimura-Nishida and Crandall-Tartar, we restrict ourselves to one space dimension. We show global existence for a quite general class of systems and under some special condition (S) we obtain information on the asymptotic behaviour and on scattering when the data have small L1 norm. The new idea lies in the introduction of some functional spaces where some products can be defined; this enables us to define an appropriate notion of solution in L1 and then use it to obtain local and global existence for data in L1 (R).
Author: Luc C. Tartar
Publisher:
ISBN:
Category : Differential equations, Hyperbolic
Languages : en
Pages : 32
Get Book Here
Book Description
We study semilinear hyperbolic systems with quadratic nonlinearities which originate in the kinetic theory of gas as a simplification of Boltzmann's equation. Local existence is well known for these equations and the main problem is to prove global existence for nonnegative bounded data. Except for the unrealistic case where a bounded invariant region exists, no result of this type is known in three space dimensions. As in all preceding results, based on the work of Mimura-Nishida and Crandall-Tartar, we restrict ourselves to one space dimension. We show global existence for a quite general class of systems and under some special condition (S) we obtain information on the asymptotic behaviour and on scattering when the data have small L1 norm. The new idea lies in the introduction of some functional spaces where some products can be defined; this enables us to define an appropriate notion of solution in L1 and then use it to obtain local and global existence for data in L1 (R).
Author: Avron Douglis
Publisher:
ISBN:
Category :
Languages : en
Pages : 150
Get Book Here
Book Description
Author: Howard E. Conner
Publisher:
ISBN:
Category : Differential equations, Hyperbolic
Languages : en
Pages : 20
Get Book Here
Book Description
Author: David Cruz-Uribe
Publisher: Springer
ISBN: 3034808402
Category : Mathematics
Languages : en
Pages : 173
Get Book Here
Book Description
This book targets graduate students and researchers who want to learn about Lebesgue spaces and solutions to hyperbolic equations. It is divided into two parts. Part 1 provides an introduction to the theory of variable Lebesgue spaces: Banach function spaces like the classical Lebesgue spaces but with the constant exponent replaced by an exponent function. These spaces arise naturally from the study of partial differential equations and variational integrals with non-standard growth conditions. They have applications to electrorheological fluids in physics and to image reconstruction. After an introduction that sketches history and motivation, the authors develop the function space properties of variable Lebesgue spaces; proofs are modeled on the classical theory. Subsequently, the Hardy-Littlewood maximal operator is discussed. In the last chapter, other operators from harmonic analysis are considered, such as convolution operators and singular integrals. The text is mostly self-contained, with only some more technical proofs and background material omitted. Part 2 gives an overview of the asymptotic properties of solutions to hyperbolic equations and systems with time-dependent coefficients. First, an overview of known results is given for general scalar hyperbolic equations of higher order with constant coefficients. Then strongly hyperbolic systems with time-dependent coefficients are considered. A feature of the described approach is that oscillations in coefficients are allowed. Propagators for the Cauchy problems are constructed as oscillatory integrals by working in appropriate time-frequency symbol classes. A number of examples is considered and the sharpness of results is discussed. An exemplary treatment of dissipative terms shows how effective lower order terms can change asymptotic properties and thus complements the exposition.
Author: Ronald E. Dean
Publisher:
ISBN:
Category :
Languages : en
Pages : 102
Get Book Here
Book Description
Author: Thomas Joseph Langan
Publisher:
ISBN:
Category : Differential equations, Partial
Languages : en
Pages : 102
Get Book Here
Book Description
Author: Howard E. Conner
Publisher:
ISBN:
Category : Differential equations, Hyperbolic
Languages : en
Pages : 14
Get Book Here
Book Description
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
Get Book Here
Book Description
The paper discusses the general structure of a class of semilinear hyperbolic systems analogous to the Boltzmann equations for a gas model with discretized velocity states, using a background of nonequilibrium theory for gas dynamics. The global existence of (nonnegative) solutions associated with nonnegative initial data is developed. Some auxiliary results on a linear conjugacy of systems and on monotonicity and smoothness properties of general (local) solutions are given.
Author: Falk Michael Hante
Publisher:
ISBN:
Category :
Languages : en
Pages : 145
Get Book Here
Book Description
Author: Thomas Y. Hou
Publisher: Springer Science & Business Media
ISBN: 3642557112
Category : Mathematics
Languages : en
Pages : 946
Get Book Here
Book Description
The International Conference on "Hyperbolic Problems: Theory, Numerics and Applications'' was held in CalTech on March 25-30, 2002. The conference was the ninth meeting in the bi-annual international series which became one of the highest quality and most successful conference series in Applied mathematics. This volume contains more than 90 contributions presented in this conference, including plenary presentations by A. Bressan, P. Degond, R. LeVeque, T.-P. Liu, B. Perthame, C.-W. Shu, B. Sjögreen and S. Ukai. Reflecting the objective of series, the contributions in this volume keep the traditional blend of theory, numerics and applications. The Hyp2002 meeting placed a particular emphasize on fundamental theory and numerical analysis, on multi-scale analysis, modeling and simulations, and on geophysical applications and free boundary problems arising from materials science and multi-component fluid dynamics. The volume should appeal to researchers, students and practitioners with general interest in time-dependent problems governed by hyperbolic equations.
