Generalized Solutions of First-Order Nonlinear PDEs

  • Alexander I. Saichev
  • Wojbor A. Woyczyński
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)


Most of the equations of mathematical physics, and in particular nonlinear first-order partial differential equations, are a result of idealizing and simplifying assumptions. This approach promotes the effectiveness and elegance of mathematical models that adequately reflect some important qualitative features of the physical phenomena under consideration. However, sooner or later, one has to pay the price for the simplifying assumptions. The influence of factors not taken into account sometimes is gradual, and does not affect the qualitative picture of the physical phenomenon, but sometimes it is abrupt, and the simplified model is unable to describe the real course of events.


Velocity Field Weak Solution Multivalued Function Density Field Particle Flow 

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Alexander I. Saichev
    • 1
    • 2
  • Wojbor A. Woyczyński
    • 3
  1. 1.Department of Management, Technology, and EconomicsETH ZürichZürichSwitzerland
  2. 2.Department of Radio PhysicsUniversity of Nizhniy NovgorodNizhniy NovgorodRussia
  3. 3.Department of Mathematics, Applied Mathematics and Statistics, and Center for Stochastic and Chaotic Processes in Science and TechnologyCase Western Reserve UniversityClevelandUSA

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