Publication: Thermal waves in absorbing media
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1988-08
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We discuss the existence of travelling-wave solutions with interfaces for the nonlinear heat equation with absorption
ut = a(um)xx – bu(n)
with a, b> 0 and m, n Є R. Several situations occur depending on the relative strength of the diffusion and absorption terms reflected by their exponents m and n. We characterize the existence of finite travelling waves in terms of m and n, show their uniqueness up to translations in space and time, and derive their velocity from the wave profile near the interface or front.
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