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

Liouville theorems and blow up behaviour in semilinear reaction diffusion systems Andreucci, D. Herrero, Miguel A. Velázquez, J.J. L. 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. 2023-06-20T17:03:33Z 2023-06-20T17:03:33Z 2023-06-20T17:03:33Z 1997 journal article https://hdl.handle.net/20.500.14352/57702 0294-1449 10.1016/S0294-1449(97)80148-5 eng Grant CRG920126. “Problemi non lineari .“ Grant PB93-0438 restricted access Elsevier (Gauthier-Villars),