Nonlinear degenerate parabolic equations with time-dependent singular potentials for Baouendi-Grushin vector fields
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| 008 | 210128e20150101xx s 000 0 eng | ||
| 024 | 7 | 0 | |a 10.1007/s10114-015-3757-z |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10114-015-3757-z | ||
| 245 | 0 | 0 | |a Nonlinear degenerate parabolic equations with time-dependent singular potentials for Baouendi-Grushin vector fields |h [Elektronische Daten] |c [Jun Han, Qian Guo] |
| 520 | 3 | |a In this paper, we are concerned with the following three types of nonlinear degenerate parabolic equations with time-dependent singular potentials: $$\begin{array}{*{20}c} {\frac{{\partial u^q }} {{\partial t}} = \nabla _\alpha \cdot \left( {\left\| z \right\|^{ - p\gamma } \left| {\nabla _\alpha u} \right|^{p - 2} \nabla _\alpha u} \right) + V(z,t)u^{p - 1} ,} \\ {\frac{{\partial u^q }} {{\partial t}} = \nabla _\alpha \cdot \left( {\left\| z \right\|^{ - 2\gamma } \nabla _\alpha u^m } \right) + V(z,t)u^m ,} \\ {\frac{{\partial u^q }} {{\partial t}} = u^\mu \nabla _\alpha \cdot \left( {u^\tau \left| {\nabla _\alpha u} \right|^{p - 2} \nabla _\alpha u} \right) + V(z,t)u^{p - 1 + \mu + \tau } } \\ \end{array}$$ in a cylinder Ω × (0, T) with initial condition u (z, 0) = u 0 (z) ≥ 0 and vanishing on the boundary ∂Ω × (0, T), where Ω is a Carnot-Carathéodory metric ball in ℝ d+k and the time-dependent singular potential function is V (z, t) ∈ L loc 1 (Ω × (0, T)). We investigate the nonexistence of positive solutions of these three problems and present our results on nonexistence. | |
| 540 | |a Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg, 2014 | ||
| 690 | 7 | |a Nonlinear degenerate parabolic equations |2 nationallicence | |
| 690 | 7 | |a Baouendi-Grushin vector fields |2 nationallicence | |
| 690 | 7 | |a positive solutions |2 nationallicence | |
| 690 | 7 | |a nonexistence |2 nationallicence | |
| 690 | 7 | |a Hardy inequality |2 nationallicence | |
| 700 | 1 | |a Han |D Jun |u Department of Applied Mathematics, Northwestern Polytechnical University, 710072, Xi'an, P. R. China |4 aut | |
| 700 | 1 | |a Guo |D Qian |u Department of Applied Mathematics, Northwestern Polytechnical University, 710072, Xi'an, P. R. China |4 aut | |
| 773 | 0 | |t Acta Mathematica Sinica, English Series |d Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society |g 31/1(2015-01-01), 123-139 |x 1439-8516 |q 31:1<123 |1 2015 |2 31 |o 10114 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10114-015-3757-z |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s10114-015-3757-z |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Han |D Jun |u Department of Applied Mathematics, Northwestern Polytechnical University, 710072, Xi'an, P. R. China |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Guo |D Qian |u Department of Applied Mathematics, Northwestern Polytechnical University, 710072, Xi'an, P. R. China |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Acta Mathematica Sinica, English Series |d Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society |g 31/1(2015-01-01), 123-139 |x 1439-8516 |q 31:1<123 |1 2015 |2 31 |o 10114 | ||