Geodesic
$L^{2}$-stability of the solutions to a nonlinear binary reaction-diffusion system of P.D.E.s
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 16 (2005) no. 4, pp. 227-238.

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The $L^{2}$-stability (instability) of a binary nonlinear reaction diffusion system of P.D.E.s - either under Dirichlet or Neumann boundary data - is considered. Conditions allowing the reduction to a stability (instability) problem for a linear binary system of O.D.E.s are furnished. A peculiar Liapunov functional $V$ linked (together with the time derivative along the solutions) by direct simple relations to the eigenvalues, is used. 
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Rionero, Salvatore. $L^{2}$-stability of the solutions to a nonlinear binary reaction-diffusion system of P.D.E.s. Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 16 (2005) no. 4, pp. 227-238. http://geodesic.mathdoc.fr/item/RLIN_2005_9_16_4_a1/

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