Generalized Solutions of Nonlinear Equations
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.
KeywordsGeneralize Solution Weak Solution Convex Hull Detonation Wave Nonlinear Partial Differential Equation
Unable to display preview. Download preview PDF.
- 1.M.J. Lighthill, Waves in Fluids, 2nd edn. (Cambridge University Press, 2002)Google Scholar
- 2.B.L. Rozhdestvenskii, N.N. Yanenko, Systems of Quasi linear Equations (Nauka, Moscow, 1978). In RussianGoogle Scholar
- 5.M.B. Vinogradova, O.V. Rudenko, A.P. Sukhorukov, Theory of Waves (Nauka, Moscow, 1979). In RussianGoogle Scholar
- 6.R. Richtmyer, Principles of Advanced Mathematical Physic, vol. 1 (Springer, Berlin, 1978)Google Scholar
- 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