Uniqueness of very singular self-similar solution of a quasilinear degenerate parabolic equation with absorption.
Díaz, Jesús Ildefonso ; Saa, José Evaristo
Publicacions Matemàtiques, Tome 36 (1992), p. 19-38 / Harvested from Biblioteca Digital de Matemáticas
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We show the uniqueness of the very singular self-similar solution of the equation

ut - Δ pum + uq = 0.

The result is carried out by studying the stationary associate equation and by introducing a suitable change of unknown. That allows to assume the zero-order perturbation term in the new equation to be monotone increasing. A careful study of the behaviour of solutions near the boundary of their support is also used in order to prove the main result.

Publié le : 1992-01-01
DMLE-ID : 3718 
@article{urn:eudml:doc:41171,
     title = {Uniqueness of very singular self-similar solution of a quasilinear degenerate parabolic equation with absorption.},
     journal = {Publicacions Matem\`atiques},
     volume = {36},
     year = {1992},
     pages = {19-38},
     zbl = {0794.35091},
     language = {en},
     url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41171}
}

Díaz, Jesús Ildefonso; Saa, José Evaristo. Uniqueness of very singular self-similar solution of a quasilinear degenerate parabolic equation with absorption.. Publicacions Matemàtiques, Tome 36 (1992) pp. 19-38. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41171/