Electronic ISBN:  9781470401849 
Product Code:  MEMO/125/599.E 
List Price:  $48.00 
MAA Member Price:  $43.20 
AMS Member Price:  $28.80 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 125; 1997; 120 ppMSC: Primary 35; 76;
Physical models of conservation form—such as the compressible NavierStokes equations, and MHD and full nonlinear elasticity equations—are not uniformly parabolic, but rather hyperbolicparabolic. This memoir gives a selfcontained analysis of nonlinear interactions of dissipation waves as well as the hyperbolic aspects of general systems. It introduces the new pointwise estimates of Green functions and coupling of nonlinear waves.
ReadershipGraduate students and research mathematicians interested in partial differential equations.

Table of Contents

Chapters

1. Introduction

2. Viscous conservation laws

3. Diffusion waves

4. Systems with diagonalizable linearizations

5. Green’s function for a $2 \times 2$ linear system

6. Green’s functions for $n \times n$ systems with applications

7. Energy estimate

8. Systems with nondiagonalizable linearizations

9. Applications to continuum mechanics


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Physical models of conservation form—such as the compressible NavierStokes equations, and MHD and full nonlinear elasticity equations—are not uniformly parabolic, but rather hyperbolicparabolic. This memoir gives a selfcontained analysis of nonlinear interactions of dissipation waves as well as the hyperbolic aspects of general systems. It introduces the new pointwise estimates of Green functions and coupling of nonlinear waves.
Graduate students and research mathematicians interested in partial differential equations.

Chapters

1. Introduction

2. Viscous conservation laws

3. Diffusion waves

4. Systems with diagonalizable linearizations

5. Green’s function for a $2 \times 2$ linear system

6. Green’s functions for $n \times n$ systems with applications

7. Energy estimate

8. Systems with nondiagonalizable linearizations

9. Applications to continuum mechanics