Asymptotic Behaviour and Blow-up of Some Unbounded Solutions for a Semilinear Heat Equation
نویسنده
چکیده
The initial-boundary value problem for the nonlinear heat equation u, = Au + Xf(u) might possibly have global classical unbounded solutions, u* = u(x, r; uS), for some "critical" initial data u*. The asymptotic behaviour of such solutions is studied, when there exists a unique bounded steady state w(x,A) for some values of L We find, for radial symmetric solutions, that u*(r,t)-*w{r) for any 0 < r < l but supu*(-,() = "*(0,t)-*°o> as t-»oo. Furthermore, if u0 > u*, where u* is some such critical initial data, then u = u(x, t; u0) blows up in finite time provided that / grows sufficiently fast.
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