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Fujita systems

Studying reaction-diffusion processes one has to consider the following semilinear system of partial differential equations:
\begin{eqnarray*}u_{jt}=\Delta u_j +f_j(u)\quad (x\in \R^n,\; t\in (0,T)\subset \R) (j=1,2,...,m)\end{eqnarray*}
with the initial condition
\begin{eqnarray*}u_j(x,0)=u_{j0}(x)\quad (x\in \R^n)\end{eqnarray*}
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