SINGULAR SOLUTIONS TO THE HEAT EQUATIONS WITH NONLINEAR ABSORPTION AND HARDY POTENTIALS
2012 ◽
Vol 14
(02)
◽
pp. 1250013
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Keyword(s):
The One
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We study the existence and nonexistence of singular solutions to the equation [Formula: see text], p > 1, in ℝN× [0, ∞), N ≥ 3, with a singularity at the point (0, 0), that is, nonnegative solutions satisfying u(x, 0) = 0 for x ≠ 0, assuming that α > -2 and [Formula: see text]. The problem is transferred to the one for a weighted Laplace–Beltrami operator with a nonlinear absorption, absorbing the Hardy potential in the weight. A classification of a singular solution to the weighted problem either as a source solution with a multiple of the Dirac mass as initial datum, or as a unique very singular solution, leads to a complete classification of singular solutions to the original problem, which exist if and only if [Formula: see text].
2005 ◽
Vol 135
(3)
◽
pp. 563-584
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2005 ◽
Vol 135
(3)
◽
pp. 563-584
2004 ◽
Vol 134
(1)
◽
pp. 39-54
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2020 ◽
Vol 21
(7-8)
◽
pp. 739-747
Keyword(s):
Keyword(s):
2001 ◽
Vol 131
(1)
◽
pp. 27-44
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