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Distribution Solutions of Nonlinear Systems of Conservation Laws

Michael Sever The Hebrew University, Jerusalem, Israel
Available Formats:
Electronic ISBN: 978-1-4704-0495-6
Product Code: MEMO/190/889.E
List Price: $72.00 MAA Member Price:$64.80
AMS Member Price: $43.20 Click above image for expanded view Distribution Solutions of Nonlinear Systems of Conservation Laws Michael Sever The Hebrew University, Jerusalem, Israel Available Formats:  Electronic ISBN: 978-1-4704-0495-6 Product Code: MEMO/190/889.E  List Price:$72.00 MAA Member Price: $64.80 AMS Member Price:$43.20
• Book Details

Memoirs of the American Mathematical Society
Volume: 1902007; 163 pp
MSC: 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 delta-shocks and singular shocks. Notwithstanding the similar form of the singularities, the analysis of delta-shocks is very different from that of singular shocks, as are the systems for which they occur. Roughly speaking, the difference is that for delta-shocks, 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. Delta-shocks
• 3. Singular shocks
• Requests

Review Copy – for reviewers who would like to review an AMS book
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Volume: 1902007; 163 pp
MSC: 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 delta-shocks and singular shocks. Notwithstanding the similar form of the singularities, the analysis of delta-shocks is very different from that of singular shocks, as are the systems for which they occur. Roughly speaking, the difference is that for delta-shocks, 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. Delta-shocks
• 3. Singular shocks
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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