eBook ISBN:  9781470404956 
Product Code:  MEMO/190/889.E 
List Price:  $72.00 
MAA Member Price:  $64.80 
AMS Member Price:  $43.20 
eBook ISBN:  9781470404956 
Product Code:  MEMO/190/889.E 
List Price:  $72.00 
MAA Member Price:  $64.80 
AMS Member Price:  $43.20 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 190; 2007; 163 ppMSC: Primary 35
The local structure of solutions of initial value problems for nonlinear systems of conservation laws is considered. Given large initial data, there exist systems with reasonable structural properties for which standard entropy weak solutions cannot be continued after finite time, but for which weaker solutions, valued as measures at a given time, exist. At any given time, the singularities thus arising admit representation as weak limits of suitable approximate solutions in the space of measures with respect to the space variable.
Two distinct classes of singularities have emerged in this context, known as deltashocks and singular shocks. Notwithstanding the similar form of the singularities, the analysis of deltashocks is very different from that of singular shocks, as are the systems for which they occur. Roughly speaking, the difference is that for deltashocks, the density approximations majorize the flux approximations, whereas for singular shocks, the flux approximations blow up faster. As against that admissible singular shocks have viscous structure.

Table of Contents

Chapters

1. General distribution solutions

2. Deltashocks

3. Singular shocks


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The local structure of solutions of initial value problems for nonlinear systems of conservation laws is considered. Given large initial data, there exist systems with reasonable structural properties for which standard entropy weak solutions cannot be continued after finite time, but for which weaker solutions, valued as measures at a given time, exist. At any given time, the singularities thus arising admit representation as weak limits of suitable approximate solutions in the space of measures with respect to the space variable.
Two distinct classes of singularities have emerged in this context, known as deltashocks and singular shocks. Notwithstanding the similar form of the singularities, the analysis of deltashocks is very different from that of singular shocks, as are the systems for which they occur. Roughly speaking, the difference is that for deltashocks, the density approximations majorize the flux approximations, whereas for singular shocks, the flux approximations blow up faster. As against that admissible singular shocks have viscous structure.

Chapters

1. General distribution solutions

2. Deltashocks

3. Singular shocks