Abstract
In this paper we prove some results concerning existence and nonexistence of global solutions of the Cauchy problem for a class of semilinear hyperbolic systems of the form
with smooth compactly supported initial data in R n. Here n ≥ 1 and H: R 2 → R is a given C 2 function. We shall call (0.1) a hyperbolic system of Hamiltonian type (see [5]). For the sake of simplicity, we shall concentrate our attention to the special case
with p, q > 1.
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Del Santo, D., Georgiev, V., Mitidieri, E. (1997). Global existence of the solutions and formation of singularities for a class of hyperbolic systems. In: Colombini, F., Lerner, N. (eds) Geometrical Optics and Related Topics. Progress in Nonlinear Differential Equations and Their Applications, vol 32. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-2014-5_7
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DOI: https://doi.org/10.1007/978-1-4612-2014-5_7
Publisher Name: Birkhäuser, Boston, MA
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