Qualitative properties of coupled parabolic systems of evolution equations

Stefano Cardanobile; Delio Mugnolo

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2008)

  • Volume: 7, Issue: 2, page 287-312
  • ISSN: 0391-173X

Abstract

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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.

How to cite

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Cardanobile, Stefano, and Mugnolo, Delio. "Qualitative properties of coupled parabolic systems of evolution equations." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 7.2 (2008): 287-312. <http://eudml.org/doc/272299>.

@article{Cardanobile2008,
abstract = {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.},
author = {Cardanobile, Stefano, Mugnolo, Delio},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {evolution equations; sesquilinear forms on Hilbert spaces; applications to parabolic problems; products of Hilbert spaces; matrices of sesquilinear mappings},
language = {eng},
number = {2},
pages = {287-312},
publisher = {Scuola Normale Superiore, Pisa},
title = {Qualitative properties of coupled parabolic systems of evolution equations},
url = {http://eudml.org/doc/272299},
volume = {7},
year = {2008},
}

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
PB - Scuola Normale Superiore, Pisa
VL - 7
IS - 2
SP - 287
EP - 312
AB - 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.
LA - eng
KW - evolution equations; sesquilinear forms on Hilbert spaces; applications to parabolic problems; products of Hilbert spaces; matrices of sesquilinear mappings
UR - http://eudml.org/doc/272299
ER -

References

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