caa a22 4500 605461023 CHVBK 20210128100241.0 cr unu---uuuuu 210128e20150101xx s 000 0 eng 10.1007/s10114-015-3757-z doi (NATIONALLICENCE)springer-10.1007/s10114-015-3757-z Nonlinear degenerate parabolic equations with time-dependent singular potentials for Baouendi-Grushin vector fields [Elektronische Daten] [Jun Han, Qian Guo] 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. Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg, 2014 Nonlinear degenerate parabolic equations nationallicence Baouendi-Grushin vector fields nationallicence positive solutions nationallicence nonexistence nationallicence Hardy inequality nationallicence Han Jun Department of Applied Mathematics, Northwestern Polytechnical University, 710072, Xi'an, P. R. China aut Guo Qian Department of Applied Mathematics, Northwestern Polytechnical University, 710072, Xi'an, P. R. China aut Acta Mathematica Sinica, English Series Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 31/1(2015-01-01), 123-139 1439-8516 31:1<123 2015 31 10114 https://doi.org/10.1007/s10114-015-3757-z text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10114-015-3757-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Han Jun Department of Applied Mathematics, Northwestern Polytechnical University, 710072, Xi'an, P. R. China aut NATIONALLICENCE 700 1- Guo Qian Department of Applied Mathematics, Northwestern Polytechnical University, 710072, Xi'an, P. R. China aut NATIONALLICENCE 773 0- Acta Mathematica Sinica, English Series Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 31/1(2015-01-01), 123-139 1439-8516 31:1<123 2015 31 10114