The Quenching Problem in the Nonlinear Heat Equations
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🧮 math.AP
math-phmath.MP
keywords
collapseequationsheatnonlinearnonlinearitiespowerproblemquenching
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In this paper we study the quenching problem in nonlinear heat equations with power nonlinearities. For nonlinearities of power p<0 and for an open set of slowly varying initial conditions we prove that the solutions will collapse in a finite time. We find the collapse profile and estimate the remainder.
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