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We apply functional analytical and variational methods in order to study well-posedness and qualitative properties of evolution equations on product Hilbert spaces. To this aim we introduce an algebraic formalism for matrices of sesquilinear mappings. We apply our results to parabolic problems of different nature: a coupled diffusive system arising in neurobiology, a strongly damped wave equation, and a heat equation with dynamic boundary conditions.
@article{ASNSP_2008_5_7_2_287_0,
author = {Cardanobile, Stefano and Mugnolo, Delio},
title = {Qualitative properties of coupled parabolic systems of evolution equations},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
pages = {287--312},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 7},
number = {2},
year = {2008},
mrnumber = {2437029},
zbl = {1179.35181},
language = {en},
url = {http://geodesic.mathdoc.fr/item/ASNSP_2008_5_7_2_287_0/}
}
TY - JOUR AU - Cardanobile, Stefano AU - Mugnolo, Delio TI - Qualitative properties of coupled parabolic systems of evolution equations JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2008 SP - 287 EP - 312 VL - 7 IS - 2 PB - Scuola Normale Superiore, Pisa UR - http://geodesic.mathdoc.fr/item/ASNSP_2008_5_7_2_287_0/ LA - en ID - ASNSP_2008_5_7_2_287_0 ER -
%0 Journal Article %A Cardanobile, Stefano %A Mugnolo, Delio %T Qualitative properties of coupled parabolic systems of evolution equations %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2008 %P 287-312 %V 7 %N 2 %I Scuola Normale Superiore, Pisa %U http://geodesic.mathdoc.fr/item/ASNSP_2008_5_7_2_287_0/ %G en %F ASNSP_2008_5_7_2_287_0
Cardanobile, Stefano; Mugnolo, Delio. Qualitative properties of coupled parabolic systems of evolution equations. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 7 (2008) no. 2, pp. 287-312. http://geodesic.mathdoc.fr/item/ASNSP_2008_5_7_2_287_0/