Self-similar solutions and Besov spaces for semi-linear Schrödinger and wave equations
Journées équations aux dérivées partielles (1999), article no. 9, 11 p.
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We prove that the initial value problem for the semi-linear Schrödinger and wave equations is well-posed in the Besov space , when the nonlinearity is of type , for . This allows us to obtain self-similar solutions, as well as to recover previously known results for the solutions under weaker smallness assumptions on the data.
@incollection{JEDP_1999____A9_0,
author = {Planchon, Fabrice},
title = {Self-similar solutions and {Besov} spaces for semi-linear {Schr\"odinger} and wave equations},
booktitle = {},
series = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
eid = {9},
pages = {1--11},
publisher = {Universit\'e de Nantes},
year = {1999},
doi = {10.5802/jedp.553},
zbl = {01810582},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.5802/jedp.553/}
}
TY - JOUR AU - Planchon, Fabrice TI - Self-similar solutions and Besov spaces for semi-linear Schrödinger and wave equations JO - Journées équations aux dérivées partielles PY - 1999 SP - 1 EP - 11 PB - Université de Nantes UR - http://geodesic.mathdoc.fr/articles/10.5802/jedp.553/ DO - 10.5802/jedp.553 LA - en ID - JEDP_1999____A9_0 ER -
%0 Journal Article %A Planchon, Fabrice %T Self-similar solutions and Besov spaces for semi-linear Schrödinger and wave equations %J Journées équations aux dérivées partielles %D 1999 %P 1-11 %I Université de Nantes %U http://geodesic.mathdoc.fr/articles/10.5802/jedp.553/ %R 10.5802/jedp.553 %G en %F JEDP_1999____A9_0
Planchon, Fabrice. Self-similar solutions and Besov spaces for semi-linear Schrödinger and wave equations. Journées équations aux dérivées partielles (1999), article no. 9, 11 p.. doi: 10.5802/jedp.553
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