Abstract
Abstract We deal with the extinction properties of the weak solutions for a p-Laplacian equation with a gradient nonlinearity. The critical extinction exponent is specified and the decay estimates of the extinction solutions are given.
Highlights
The main aim of this paper is devoted to studying the extinction properties of the weak solutions for the following p-Laplacian equation
Generally there is no classical solution and we introduce the definition of the weak solution for problem (1.1) as follows
Assume that 0 < q + l < p − 1, for any nonzero nonnegative initial data u0, problem (1.1) admits at least one non-extinction solution provided that μ is sufficiently large
Summary
. Recently, under decay estimates as the restrictive condition N > p, Liu and Mu [33,34] considered problem (1.1) with l = 0 and proved that q = p − 1 is the critical extinction exponent of the nonnegative weak solution. Assume that 0 < q + l < p − 1, for any nonzero nonnegative initial data u0, problem (1.1) admits at least one non-extinction solution provided that μ is sufficiently large. P , the nonnegative weak solution of problem (1.1) vanishes in finite time p+2 provided that μ is sufficiently small. (2) For any nonzero nonnegative initial data u0, problem (1.1) admits at least one non-extinction solution provided that μ is sufficiently large. Theorems 1.2, 1.3, and 1.4 generalize and extend the previous results in [7,30,31,33,34] to a more general case
Sign-in/Register to view highlights & summary 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.
