Self-similar solutions and Besov spaces for semi-linear Schrödinger and wave equations
Planchon, Fabrice
Journées équations aux dérivées partielles, (1999), p. 1-11 / Harvested from Numdam
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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 B ˙ 2 n 2-2 p,∞ (𝐑 n ), when the nonlinearity is of type u p , for p∈𝐍. 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.

Publié le : 1999-01-01
@article{JEDP_1999____A9_0,
     author = {Planchon, Fabrice},
     title = {Self-similar solutions and Besov spaces for semi-linear Schr\"odinger and wave equations},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     year = {1999},
     pages = {1-11},
     zbl = {01810582},
     language = {en},
     url = {http://dml.mathdoc.fr/item/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), pp. 1-11. http://gdmltest.u-ga.fr/item/JEDP_1999____A9_0/

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