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equation

##
Fujita systems

Studying reaction-diffusion processes one has to consider the following
semilinear system of partial differential equations:
with the initial condition
In 1981 F. B. Weissler suggested to construct subsolutions and supersolutions.
Confere his paper *Existence and nonexistence of global solutions for
semilinear heat equation* Israel J. Math. 38, 29-40. More recently such
systems attract considerable attention. The main problem which is connected
with Fujita systems is the study of global existence and finite time blow-up
of solutions.

**A late reference**: G. Lu and B.D. Sleeman, (1994) *Subsolutions
and Supersolutions to systems of parabolic equations with application to
genberalized Fujita-Type systems*. MMAS Vol 17, 1005-1016.

collected and worked out by Wolfgang Sprößig, TU-Bergakademie
Freiberg