caa a22 4500 475796918 CHVBK 20180406123727.0 cr unu---uuuuu 170329e20000101xx s 000 0 eng 10.1007/PL00001503 doi (NATIONALLICENCE)springer-10.1007/PL00001503 A nonlinear degenerate diffusion equation not in divergence form [Elektronische Daten] [S. Wang, M. Wang, Ch.-h. Xie] Abstract.: We consider positive solution of the nonlinear degenerate diffusion equation $u_t=u^p(\Delta u+u)$ with Dirichlet boundary condition and $p>1$ . It is proved that all positive solutions exist globally if and only if $\lambda_1\ge 1$ , where $\lambda _1$ is the first eigenvalue of $-\Delta$ on $\Omega$ with homogeneous Dirichlet boundary condition. Birkhäuser Verlag, Basel,, 2000 Key words.Degenerate diffusion equation, global solution, blow up, upper and lower solutions method nationallicence Wang S. Institute of Mathematics, Academia Sinica, Beijing 100080, China, and Department of Mathematics, Henan University, Kaifeng 475001, China, CN aut Wang M. Department of Applied Mathematics, Southeast University, Nanjing 210018, China, CN aut Xie Ch.-h Department of Mathematics, Nanjing University, Nanjing 210093, China, CN aut https://doi.org/10.1007/PL00001503 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/PL00001503 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Wang S. Institute of Mathematics, Academia Sinica, Beijing 100080, China, and Department of Mathematics, Henan University, Kaifeng 475001, China, CN aut NATIONALLICENCE 700 1- Wang M. Department of Applied Mathematics, Southeast University, Nanjing 210018, China, CN aut NATIONALLICENCE 700 1- Xie Ch.-h Department of Mathematics, Nanjing University, Nanjing 210093, China, CN aut Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer