Abstract
We study the geometry of the supports of solutions of the Cauchy-Dirichlet problem for a wide class of quasi-linear degenerate parabolic equations of any order, whose model representative is the equation of non-stationary filtration with non-linear absorption: In the cases when and , which correspond to “fast” and “slow” diffusion, we find conditions on the behaviour of the initial function in a neighbourhood of the boundary of its support that ensure the effect of finite and infinite inertia of the support of an arbitrary energy solution; these conditions are, in a certain sense, exact. We establish a condition for the reverse motion of the front of the support boundary.
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.
