On the influence of damping in hyperbolic equations with parabolic degeneracy (original) (raw)
2011, Quarterly of Applied Mathematics
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In this talk we shall review some recent results about qualitative behavior of smooth solutions to the Cauchy problem for general hyperbolic symmetrizable m-dimensional systems of balance laws of the form ut+ m∑ α= 1 (fα (u)) xα= g (u),(1) with the initial condition u (x, 0)= u0 (x),(2) where u=(u1, u2)∈ Ω⊆ Rn1× Rn2, with n1+ n2= n. We assume that there are n1 conservation laws in the system, namely that we can take g (u)=
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