Solution blowup for systems of shallow-water equations
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We consider initial-boundary value problems for systems of shallow-water equations. Using the testfunction method proposed by Pokhozhaev and Mitidieri, we study the effects of the boundary values and initial conditions on the occurrence, duration, and rate of blowup of the solutions of these problems. Under natural boundary conditions, we prove the existence of blowup in one- and two-dimensional problems in bounded and unbounded regions with dissipation and dispersion.
Keywordsinitial-boundary value problem finite-time blowup shallow water approximation
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- 4.B. L. Rozhdestvenskij and N. N. Yanenko, Systems of Quasilinear Equations and their Applications to Gas Dynamics [in Russian], Nauka, Moscow (1968); English transl. (Transl. Math. Monogr., Vol. 55), Amer. Math. Soc., Providence, R. I. (1983).Google Scholar
- 5.L. D. Landau and E. M. Lifshitz, Fluid Mechanics [in Russian], Nauka, Moscow (1986); English transl. prev. ed. (Vol. 6 of Course of Theoretical Physics), Pergamon, London (1959).Google Scholar
- 12.A. N. Kolmogorov and S. V. Fomin, Elements of the Theory of Functions and Functional Analysis [in Russian], Fizmatlit, Moscow (2006); English transl. prev. ed., Dover, New York (1999).Google Scholar