After reviewing some of the properties of wavelet bases, and in particular the property of characterisation of function spaces via wavelet coefficients, we describe two new approaches to, respectively, stabilisation of numerically unstable PDE's and to non linear (adaptive) solution of PDE's, which are made possible by these properties.
Dopo aver ricordato alcune delle proprietà delle basi di wavelets, ed in particolare la proprietà di caratterizzazione di spazi funzionali tramite coefficienti wavelet, descriviamo due nuovi approcci rispettivamente alla stabilizzazione di problemi numericamente instabili ed alla soluzione nonlineare (adattativa) di equazioni differenziali alle derivate parziali, che sono resi possibili da dette proprietà.
@article{BUMI_2005_8_8B_3_569_0,
author = {Silvia Bertoluzza},
title = {Recent developments in wavelet methods for the solution of PDE's},
journal = {Bollettino dell'Unione Matematica Italiana},
volume = {8-A},
year = {2005},
pages = {569-590},
mrnumber = {2182416},
language = {en},
url = {http://dml.mathdoc.fr/item/BUMI_2005_8_8B_3_569_0}
}
Bertoluzza, Silvia. Recent developments in wavelet methods for the solution of PDE's. Bollettino dell'Unione Matematica Italiana, Tome 8-A (2005) pp. 569-590. http://gdmltest.u-ga.fr/item/BUMI_2005_8_8B_3_569_0/
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