Qualitative properties of solutions to semilinear heat equations with singular initial data
Southwest Texas State University, Department of Mathematics
This article concerns the nonnegative solutions to the Cauchy problem ut - ∆u + b(x, t) |u|p-1 u = 0 in ℝN x (0, ∞), u(x, 0) = u0(x) in ℝN. We investigate how the comparison principle, extinction in finite time, instantaneous shrinking of support, and existence of solutions depend on the behaviour of the coefficient b(x, t).
Comparison principle, Extinction, Shrinking of support, Existence
Li, J. (2004). Qualitative properties of solutions to semilinear heat equations with singular initial data. <i>Electronic Journal of Differential Equations, 2004</i>(53), pp. 1-12.