Abstract:
Accurate (best possible) upper estimates are obtained for the amplitude and length of support of unbounded solutions of the quasilinear degenerate parabolic equation of non-linear heat conduction with a source. The estimates are established by means of a special “comparison by intersections” technique with an exact non-invariant solution of the equation with the same existence time. This comparison, moreover, illustrates the fact that the Cauchy problem for the equation with a delta-function as the initial datum is solvable.
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