Data di Pubblicazione:
2012
Citazione:
On well-posedness of the semilinear heat equation on the sphere / F. Punzo. - In: JOURNAL OF EVOLUTION EQUATIONS. - ISSN 1424-3199. - 12:3(2012), pp. 571-592.
Abstract:
We are concerned with existence, uniqueness and nonuniqueness of nonnegative solutions to the semilinear heat equation in open subsets of the n-dimensional sphere. Existence and uniqueness results are obtained using L p → L q estimates for the semigroup generated by the Laplace-Beltrami operator. Moreover, under proper assumptions on the nonlinear function, we establish nonuniqueness of weak solutions, when n ≥ 3; to do this, we shall prove uniqueness of positive classical solutions and nonuniqueness of singular solutions of the corresponding semilinear elliptic problem.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Laplace-Beltrami operator; Semigroup theory; Semilinear elliptic equations; Semilinear parabolic equations; Singular solutions
Elenco autori:
F. Punzo
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