On long time behavior of periodic entropy solutions of a degenerate non-linear parabolic equation
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🧮 math.AP
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degenerateentropyequationfunctionparabolictravelingwaveasymptotic
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We prove the asymptotic convergence of a space-periodic entropy solution of a one-dimensional degenerate parabolic equation to a traveling wave. It is also shown that on a segment containing the essential range of the limit profile the flux function is linear (with the slope equaled to the speed of the traveling wave) and the diffusion function is constant.
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