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

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

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},
     publisher = {mathdoc},
     volume = {Ser. 9, 16},
     number = {4},
     year = {2005},
     zbl = {1150.35012},
     mrnumber = {MR2255006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RLIN_2005_9_16_4_a1/}
}
TY  - JOUR
AU  - Rionero, Salvatore
TI  - $L^{2}$-stability of the solutions to a nonlinear binary reaction-diffusion system of P.D.E.s
JO  - Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni
PY  - 2005
SP  - 227
EP  - 238
VL  - 16
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/RLIN_2005_9_16_4_a1/
LA  - en
ID  - RLIN_2005_9_16_4_a1
ER  - 
%0 Journal Article
%A Rionero, Salvatore
%T $L^{2}$-stability of the solutions to a nonlinear binary reaction-diffusion system of P.D.E.s
%J Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni
%D 2005
%P 227-238
%V 16
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/RLIN_2005_9_16_4_a1/
%G en
%F RLIN_2005_9_16_4_a1
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/