Global solutions of semilinear parabolic equations on negatively curved Riemannian manifolds

DOI10.1007/s12220-019-00289-xzbMath1461.35130arXiv1707.08498OpenAlexW2975658622WikidataQ115376759 ScholiaQ115376759MaRDI QIDQ2659010

Fabio Punzo

Publication date: 25 March 2021

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1707.08498

zbMATH Keywords

spectral analysisground statessectional curvaturessub-supersolutions

Mathematics Subject Classification ID

Heat and other parabolic equation methods for PDEs on manifolds (58J35) Blow-up in context of PDEs (35B44) Semilinear parabolic equations (35K58) Heat kernel (35K08) Comparison principles in context of PDEs (35B51) PDEs on manifolds (35R01)

Related Items

Global solutions of semilinear parabolic equations with drift term on Riemannian manifolds, Solvability of a semilinear heat equation on Riemannian manifolds, Non-linear heat equation on the hyperbolic space: global existence and finite-time blow-up, Existence of a sign-changing weak solution to doubly nonlinear parabolic equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Nonexistence of solutions to parabolic differential inequalities with a potential on Riemannian manifolds
• The Fujita exponent for the Cauchy problem in the hyperbolic space
• Blow-up of solutions to semilinear parabolic equations on Riemannian manifolds with negative sectional curvature
• On the critical exponent for reaction-diffusion equations
• Existence and non-existence of global solutions for a semilinear heat equation
• The porous medium equation with large initial data on negatively curved Riemannian manifolds
• Blow-up results for nonlinear parabolic equations on manifolds
• The porous medium equation with measure data on negatively curved Riemannian manifolds
• A note on semilinear heat equation in hyperbolic space
• An upper bound to the spectrum of \(\Delta\) on a manifold of negative curvature
• Maximum Principles and Geometric Applications
• The Role of Critical Exponents in Blowup Theorems
• Differential equations on riemannian manifolds and their geometric applications
• Analytic and geometric background of recurrence and non-explosion of the Brownian motion on Riemannian manifolds
• Riemannian geometry