RT Journal Article
T1 Liouville theorems and blow up behaviour in semilinear reaction diffusion systems
A1 Andreucci, D.
A1 Herrero, Miguel A.
A1 Velázquez, J.J. L.
AB This paper is concerned with positive solutions of the semilinear system: (S) {u(t) = Δu + v(p), p ≥ 1, v(t) = Δv + u(q), q ≥ 1, which blow up at x = 0 and t = T < ∞. We shall obtain here conditions on p, q and the space dimension N which yield the following bounds on the blow up rates: (1) u(x, t) ≤ C(T - t)(-p + 1/pq - 1), v(x, t) ≤ C(T - t)(-q + 1/pq - 1), for some constant C > 0. We then use (1) to derive a complete classification of blow up patterns. This last result is achieved by means of a parabolic Liouville theorem which we retain to be of some independent interest. Finally, we prove the existence of solutions of (S) exhibiting a type of asymptotics near blow up which is qualitatively different from those that hold for the scalar case.
PB Elsevier (Gauthier-Villars),
SN 0294-1449
YR 1997
FD 1997
LK https://hdl.handle.net/20.500.14352/57702
UL https://hdl.handle.net/20.500.14352/57702
LA eng
NO NATO
NO MURST 40%
NO DGICYT
DS Docta Complutense
RD 19 abr 2025