2026-06-08T14:02:48Zhttps://docta.ucm.es/rest/oai/requestoai: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.
517.956.4
539.2
Semilinear systems
reaction diffusion equations
asymptotic behaviour
Liouville theorems
a priori estimates
parabolic equations
heat-equations
Ecuaciones diferenciales
1202.07 Ecuaciones en Diferencias
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.
NATO
MURST 40%
DGICYT
Depto. de Análisis Matemático y Matemática Aplicada
Fac. de Ciencias Matemáticas
TRUE
pub
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
application/pdf
Elsevier (Gauthier-Villars),