JournalszaaVol. 24, No. 1pp. 179–187

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

  • Yong Zhou

    Shanghai University of Finance and Economics, China
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Abstract

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)0a(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)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.

Cite this article

Yong Zhou, Global Nonexistence for a Quasilinear Evolution Equation with a Generalized Lewis Function. Z. Anal. Anwend. 24 (2005), no. 1, pp. 179–187

DOI 10.4171/ZAA/1236