Abstract
The present paper is devoted to the study of stationary solutions of a nonlinear degenerate diffusion equation involving a nonlocal convection term, which represents a mathematical model for spatially aggregating phenomena of populations. The equation has two ecological parameters:m>1 for the diffusion process and 0≦r≦∞ for the aggregating process expressed by the convection term. For the special case ofm=2, this paper gives all stationary solutions of the one-parameter family {P(2,r)} of the equations. The result asserts thatP(2,r) has no non-trivial stationary solution when $$0 \leqq r \leqq \sqrt 2 $$ , whileP(2,r) has many pulse-like stationary solutions when $$r > \sqrt 2 $$ . The paper also states a partial result for the general case ofm, and offers a view of the global structure of stationary solutions ofP(m, r).
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.
