We study the Cauchy problem for the semilinear heat equation on Riemannian manifolds. Propagation and extinction of solutions are addressed, supposing that the nonlinear forcing term is either of KPP type or of bistable type. In particular, we highlight the influence both of sectional curvatures and of Ricci curvature on such phenomena.
Propagation and extinction of fronts for semilinear parabolic equations on negatively curved Riemannian manifolds / F. Punzo. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - 131:(2016), pp. 325-345. [10.1016/j.na.2015.09.010]
Propagation and extinction of fronts for semilinear parabolic equations on negatively curved Riemannian manifolds
F. Punzo
2016
Abstract
We study the Cauchy problem for the semilinear heat equation on Riemannian manifolds. Propagation and extinction of solutions are addressed, supposing that the nonlinear forcing term is either of KPP type or of bistable type. In particular, we highlight the influence both of sectional curvatures and of Ricci curvature on such phenomena.
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