Diffusion phenomenon for indirectly damped hyperbolic systems coupled by velocities in exterior domains
2020 ◽
Vol 17
(03)
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pp. 475-500
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We consider a system of two coupled wave equations in an exterior domain, where only one equation is directly damped. We prove that the solutions are [Formula: see text]-approximated by special functions, classified into three patterns depending on the values of the damping and the coupling terms, as well as on the speeds of the waves. In particular, when the damping term is sufficiently large, the waves are asymptotically equal to solutions of parabolic-type equations as [Formula: see text]. This result generalizes the standard diffusion phenomenon for directly damped hyperbolic systems.
1972 ◽
Vol 72
(2)
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pp. 285-297
1967 ◽
Vol 63
(4)
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pp. 1229-1246
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Keyword(s):
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2007 ◽
Vol 256
(3)
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pp. 521-549
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2013 ◽
Vol 87
(12)
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pp. 1233-1241
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