Title: | On the strong comparison principle for degenerate elliptic problems with convection |
Authors: | Benedikt, Jiří Girg, Petr Kotrla, Lukáš Takáč, Peter |
Citation: | BENEDIKT, J. GIRG, P. KOTRLA, L. TAKÁČ, P. On the strong comparison principle for degenerate elliptic problems with convection. Journal of Mathematical Analysis and Applications, 2022, roč. 514, č. 1, s. 1-21. ISSN: 0022-247X |
Issue Date: | 2022 |
Publisher: | Academic Press |
Document type: | článek article |
URI: | 2-s2.0-85130887430 http://hdl.handle.net/11025/49745 |
ISSN: | 0022-247X |
Keywords in different language: | Quasilinear parabolic equation;Degenerate p-Laplacian;Examples and counterexamples to strong comparison principle;Hopf’s boundary point lemma |
Abstract: | The weak and strong comparison principles (WCP and SCP, respectively) are investigated for quasilinear elliptic boundary value problems with the p-Laplacian in one space dimension, Δp(u) =d/dx(|u'|p−2u'). We treat the “degenerate” case of 2 <p <∞ and allow also for the nontrivial convection velocity b :[−1, 1] →R in the underlying domain Ω =(−1, 1). We establish the WCP under a rather general, “natural sufficient condition” on the convection velocity, b(x), and the reaction function, ϕ(x, u). Furthermore, we establish also the SCP under a number of various additional hypotheses. In contrast, with these hypotheses being violated, we construct also a few rather natural counterexamples to the SCP and discuss their applications to an interesting classical problem of fluid flow in porous medium, “seepage flow of fluids in inclined bed”. Our methods are based on a mixture of classical and new techniques. |
Abstract in different language: | The weak and strong comparison principles (WCP and SCP, respectively) are investigated for quasilinear elliptic boundary value problems with the p-Laplacian in one space dimension, Δp(u) =d/dx(|u'|p−2u'). We treat the “degenerate” case of 2 <p <∞ and allow also for the nontrivial convection velocity b :[−1, 1] →R in the underlying domain Ω =(−1, 1). We establish the WCP under a rather general, “natural sufficient condition” on the convection velocity, b(x), and the reaction function, ϕ(x, u). Furthermore, we establish also the SCP under a number of various additional hypotheses. In contrast, with these hypotheses being violated, we construct also a few rather natural counterexamples to the SCP and discuss their applications to an interesting classical problem of fluid flow in porous medium, “seepage flow of fluids in inclined bed”. Our methods are based on a mixture of classical and new techniques. |
Rights: | Plný text je přístupný v rámci univerzity přihlášeným uživatelům. © Elsevier |
Appears in Collections: | Články / Articles (NTIS) Články / Articles (KMA) OBD |
Files in This Item:
File | Size | Format | |
---|---|---|---|
1-s2.0-S0022247X22002815-main.pdf | 537,51 kB | Adobe PDF | View/Open Request a copy |
Please use this identifier to cite or link to this item:
http://hdl.handle.net/11025/49745
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.