Data di Pubblicazione:
2011
Citazione:
On well-posedness of semilinear parabolic and elliptic problems in the hyperbolic space / F. Punzo. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - 251:7(2011), pp. 1972-1989.
Abstract:
We investigate existence and uniqueness of solutions to semilinear parabolic and elliptic equations in bounded domains of the n-dimensional hyperbolic space (n≥3). Lp→Lq estimates for the semigroup generated by the Laplace-Beltrami operator are obtained and then used to prove existence and uniqueness results for parabolic problems. Moreover, under proper assumptions on the nonlinear function, we establish uniqueness of positive classical solutions and nonuniqueness of singular solutions of the elliptic problem; furthermore, for the corresponding semilinear parabolic problem, nonuniqueness of weak solutions is stated.
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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