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oai:docta.ucm.es:20.500.14352/577022023-08-10T16:20:22Zcom_20.500.14352_14col_20.500.14352_15

Andreucci, D. Herrero, Miguel A. Velázquez, J.J. L. 2023-06-20T17:03:33Z 2023-06-20T17:03:33Z 1997 0294-1449 10.1016/S0294-1449(97)80148-5 https://hdl.handle.net/20.500.14352/57702 http://www.sciencedirect.com/science/article/pii/S0294144997801485 http://www.sciencedirect.com 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. eng restricted access Liouville theorems and blow up behaviour in semilinear reaction diffusion systems journal article