Threshold and strong threshold solutions of a semilinear parabolic equation
classification
🧮 math.AP
keywords
solutionspositiveequationglobalthresholdtimebehaviorblow
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If $p>1+2/n$ then the equation $u_t-\Delta u = u^p, \quad x\in{\mathbb R}^n,\ t>0,$ possesses both positive global solutions and positive solutions which blow up in finite time. We study the large time behavior of radial positive solutions lying on the borderline between global existence and blow-up.
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