Large-time behavior of solutions to certain quasilinear parabolic equations in several space dimensions

Authors:
Patricia Bauman and Daniel Phillips

Journal:
Proc. Amer. Math. Soc. **96** (1986), 237-240

MSC:
Primary 35B40; Secondary 35K55

MathSciNet review:
818451

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Abstract: We consider the Cauchy problem, for with . For , suppose and where is piecewise constant and as . A result of Il'in and Oleinik states that if is an entropy solution of , then approaches a traveling wave solution, , as , with as . We give two examples which show that this result does not hold for .

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DOI:
https://doi.org/10.1090/S0002-9939-1986-0818451-2

Article copyright:
© Copyright 1986
American Mathematical Society