The EMS Publishing House is now EMS Press and has its new home at ems.press.

Please find all EMS Press journals and articles on the new platform.

Zeitschrift für Analysis und ihre Anwendungen


Full-Text PDF (160 KB) | Metadata | Table of Contents | ZAA summary
Volume 24, Issue 1, 2005, pp. 179–187
DOI: 10.4171/ZAA/1236

Published online: 2005-03-31

Global Nonexistence for a Quasilinear Evolution Equation with a Generalized Lewis Function

Yong Zhou[1]

(1) Shanghai University of Finance and Economics, China

We consider the following quasilinear parabolic equation \begin{eqnarray*} a(x,t) u_t-\mbox{\rm div}\left(|\nabla u|^{m-2} \nabla u \right)=f(u), \end{eqnarray*} where $a(x,t) \geq 0$ is a generalized Lewis function. The main result is that the solution blows up in finite time if the initial datum $u(x,0)$ possesses suitable positive energy. Moreover, we have a precise estimate for the lifespan of the solution in this case. Blowup of solutions with vanishing initial energy is considered also.

Keywords: Global nonexistence, quasilinear evolution equation

Zhou Yong: Global Nonexistence for a Quasilinear Evolution Equation with a Generalized Lewis Function. Z. Anal. Anwend. 24 (2005), 179-187. doi: 10.4171/ZAA/1236