Global Existence Theory for a General Class of Hyperbolic Balance Laws
Vol. 10 No. 2 (2015) P.143~P.170
We consider a general system of hyperbolic balance laws in m space dimensions
(m $\geq$ 1). Under a set of conditions we establish the existence of global solutions for
the Cauchy problem when initial data are small perturbations of a constant equilibrium
state. The proposed assumptions in this paper are different from those in literature for
the system. Instead, our assumptions are parallel to those used in the study of hyperbolic-parabolic systems. In one space dimension our assumptions are natural extensions of those used in the study of the Green’s function of the linearized system. They are also sufficient to the study of large time behavior in the pointwise sense for the nonlinear system, carried
out in a different paper.
hyperbolic balance laws, global existence, structural conditions, energy estimate.
MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 35L45, 35L60, 35Q35.
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Revised : 2015-04-28