Grow-up for a quasilinear heat equation with a localized reaction in higher dimensions Articles uri icon

publication date

  • September 2018

start page

  • 805

end page

  • 832


  • 3


  • 31

International Standard Serial Number (ISSN)

  • 1139-1138

Electronic International Standard Serial Number (EISSN)

  • 1988-2807


  • We study the behaviour of nonnegative global solutions to the quasilinear heat equation with a reaction localized in a ball u(t) = Delta(m)(u) + a(x) u(p), for m > 0, 0 < p <= max{1, m}, a(x) = 1(BL) (x), 0 < L < infinity and N >= 2. We study when the solutions are bounded or unbounded. In particular we show that the precise value of the length L plays a crucial role in the critical case p = m for N >= 3. We also obtain the asymptotic behaviour of unbounded solutions and prove that the grow-up rate is different in most of the cases to the one obtained when L = infinity.


  • quasilinear diffusion equations; localized reaction; grow-up