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 Cet article a éte moissonné depuis la source Biblioteca Digitale Italiana di Matematica

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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. 
@article{RLIN_2005_9_16_4_a1,
     author = {Rionero, Salvatore},
     title = {$L^{2}$-stability of the solutions to a nonlinear binary reaction-diffusion system of {P.D.E.s}},
     journal = {Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni},
     pages = {227--238},
     year = {2005},
     volume = {Ser. 9, 16},
     number = {4},
     zbl = {1150.35012},
     mrnumber = {MR2255006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RLIN_2005_9_16_4_a1/}
}
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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/