Generalized Solutions of Nonlinear Equations

  • S. N. Gurbatov
  • O. V. Rudenko
  • A. I. Saichev
Part of the Nonlinear Physical Science book series (NPS)


Equations of mathematical physics and, in particular, nonlinear partial differential equations of the first order appear as a result of certain idealizations. This allows one to achieve elegance of mathematical models, a possibility to use them in order to predict, in an adequately quantitative way, important aspects of various real world phenomena. But any idealizations come at a cost. Factors unaccounted for by these idealizations gradually, and sometimes abruptly, begin to dominate, while the initial models cease to be able to describe what actually happens.


Generalize Solution Weak Solution Convex Hull Detonation Wave Nonlinear Partial Differential Equation 
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  1. 1.
    M.J. Lighthill, Waves in Fluids, 2nd edn. (Cambridge University Press, 2002)Google Scholar
  2. 2.
    B.L. Rozhdestvenskii, N.N. Yanenko, Systems of Quasi linear Equations (Nauka, Moscow, 1978). In RussianGoogle Scholar
  3. 3.
    G.B. Whitham, Linear and Nonlinear Waves (Wiley, New York, 1974)zbMATHGoogle Scholar
  4. 4.
    O.V. Rudenko, S.I. Soluyan, Theoretical Foundations of Nonlinear Acoustics (Plenum, New-York, 1977)zbMATHGoogle Scholar
  5. 5.
    M.B. Vinogradova, O.V. Rudenko, A.P. Sukhorukov, Theory of Waves (Nauka, Moscow, 1979). In RussianGoogle Scholar
  6. 6.
    R. Richtmyer, Principles of Advanced Mathematical Physic, vol. 1 (Springer, Berlin, 1978)Google Scholar
  7. 7.
    W.E., Y. Rykov, Y. Sinai, Generalized variational principles, global weak solutions and behavior with random initial data for systems of conservation laws arising in adhesion particle dynamics, Commun. Math. Phys. 177, 349–380 (1996)Google Scholar

Copyright information

© Higher Education Press, Beijing and Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • S. N. Gurbatov
    • 1
  • O. V. Rudenko
    • 2
  • A. I. Saichev
    • 3
  1. 1.Radiophysics DepartmentNizhny Novgorod State UniversityNizhny NovgorodRussia
  2. 2.Physics DepartmentMoscow State UniversityMoscowRussia
  3. 3.Radiophysics DepartmentNizhny Novgorod State UniversityNizhny NovgorodRussia

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