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A reaction-diffusion system modelling the post irridiation oxydation of an isotactic polypropylene. (English) Zbl 0767.35037

The authors deal with a reaction diffusion system which is some chemical model, i.e. \[ \partial_ t u_ i-\mu_ i \partial_{xx}u_ i=F_ i(U)\quad\text{in}\quad (0,\infty)\times(0,1) \qquad (i=1,2,3,4). \] \(U=(u_ 1,u_ 2,u_ 3,u_ 4)\) where the nonlinear terms are given by \[ F_ 1(U)=-k_ 1 u_ 1 u_ 2+k_ 2U_ 3^ 2, \qquad F_ 2(U)=- k_ 1 u_ 1 u_ 2-2k_ 6 u_ 2^ 2-k_ 5 u_ 3 u_ 2+k_ 3 u_ 3+k_ 8 u_ 4, \]
\[ F_ 3(U)=k_ 1 u_ 1 u_ 2-k_ 5 u_ 2 u_ 3- (k_ 2+k_ 3)u_ 3-2k_ 3 u_ 3^ 2, \qquad F_ 4(U)=2k_ 3 u_ 3^ 2-(k_ 7+k_ 8)u_ 4. \] It is shown that for any nonnegative initial condition, there exists a unique global classical solution which converges to 0 when \(t\to\infty\). Some components decay exponentially and others decay polynomially.
Reviewer: S.Jimbo (Tsushima)

MSC:

35K57 Reaction-diffusion equations
35B40 Asymptotic behavior of solutions to PDEs
92E20 Classical flows, reactions, etc. in chemistry
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