Abstract
A class of semilinear heat flows with general nonlinear reaction terms is considered on complete Riemannian manifolds with Ricci curvature bounded from below. Two types of (space-time and space only) gradient estimates are established for positive solutions to the flow, and the corresponding Harnack inequalities are obtained to allow for comparison of solutions. Some specific examples of the reaction term such as logarithmic reaction, Fisher-KPP and Allen-Cahn equations are discussed as applications of the estimates so derived. Referring to logarithmic nonlinearities, some discussions are made on Liouville type properties of bounded solutions.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
