Large time estimates for solutions to the porous medium equation with nonintegrable data via comparison
1985 ◽
Vol 100
(1-2)
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pp. 1-10
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SynopsisWe consider the Cauchy problem for the porous medium equation in one space dimension, with initial data which are locally integrable. We measure the asymptotic behaviour of the initial data near infinity in an integral sense and relate this to the pointwise rate of growth or decay of solution for large time. The emphasis is on a novel comparison method wherein the initial data are rearranged on the ×-axis to form a sequence of Dirac δ-masses. By using the explicit solution in the latter case, we derive upper and lower bounds for the solution to the original problem by comparisons.
1974 ◽
pp. 363-367
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1990 ◽
Vol 84
(1)
◽
pp. 183-203
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1981 ◽
Vol 39
(3)
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pp. 378-412
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1991 ◽
Vol 155
(2)
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pp. 345-363
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2001 ◽
Vol 26
(5-6)
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pp. 841-858
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