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  • 130pp. Published March 2018
  • Scientific Research Publishing, Inc., USA
  • Category: Physics & Mathematics
  • ISBN: 978-1-61896-443-4
  • (Paperback) USD 89.00
  • ISBN: 978-1-61896-444-1
  • (E-Book) USD 29.00

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Admissibility of Weak Solutions of Multidimensional Nonlinear Systems of Conservation Laws
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Admissible solutions of nonlinear systems of conservation laws in arbitrary dimensions are identified as points in the range of boundedly Frechet differentiable map of boundary data into weak solutions. For Cauchy problems for scalar conservation laws or hyperbolic systems in one space dimension, admissibility so determined agrees fairly closely with familiar entropy conditions.


For systems in higher dimensions, however, the set of admissible weak solutions is materially smaller than might be anticipated, computational evidence to the contrary notwithstanding. Such is provably the case for Cauchy problems for hyperbolic systems, and is strongly suggested by results obtained for reduced systems determining stationary or self-similar solutions.
Components of the Book:
  • FRONT MATTER
  • Chapter 1. Introduction and Summary
  • Chapter 2. Notation and Problem Formulation
  • Chapter 3. Stability and Admissibility
    • 3.1. Proof of Admissibility
    • 3.2. Continuation of Stability and Admissibility
    • 3.3. A Toy Example
  • Chapter 4. Scalar Conservation Laws
  • Chapter 5. The One-Space Dimensional Cauchy Problem
  • Chapter 6. Stability Failure in Higher Dimensions
  • Chapter 7. Nonhyperbolic Systems
    • 7.1. An Euler System
    • 7.2. Statement of Results
    • 7.3. Proof of Stability
    • 7.4. Proof of Admissibility
  • Chapter 8. The Symmetric p-System
    • 8.1. The Test Space
    • 8.2. Proof of Theorem 8.1
    • 8.3. Proof of Lemma 8.6
    • 8.4. Admissible Solutions
  • BACK MATTER
Readership: Experts in this area: Mathematics, specific area of partial differential equations.
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