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Decay of periodic solutions of \(\partial u/\partial t + \partial f(u)/\partial x= 0\). (English) Zbl 0269.35011

MSC:
35F20 Nonlinear first-order PDEs
35B10 Periodic solutions to PDEs
35B40 Asymptotic behavior of solutions to PDEs
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[1] \scJ. Glimm and P. D. Lax, Decay of solutions of systems of hyperbolic conservation laws, A. E. C. Research and Development Report NYO-1480-115. · Zbl 0146.33803
[2] Douglis, A, An ordering principle and generalized solutions of certain quasi-linear differential equations, Comm. pure appl. math., 12, 87-112, (1959) · Zbl 0084.29503
[3] Ballou, D.P, Solutions to nonlinear hyperbolic Cauchy problems without convexity conditions, Trans. amer. math. soc., 152, 441-460, (1970) · Zbl 0207.40401
[4] Oleinik, O.A, Uniqueness and stability of the generalized solution of the Cauchy problem for a quasi-linear equation, Trans. amer. math. soc. trans. ser., 33, 285-290, (1963), (2) · Zbl 0132.33303
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