JournalszaaVol. 17, No. 1pp. 89–102

An Example of Blowup for a Degenerate Parabolic Equation with a Nonlinear Boundary Condition

  • Michel Chipot

    Universität Zürich, Switzerland
  • Ján Filo

    Comenius University, Bratislava, Slovak Republic
An Example of Blowup for a Degenerate Parabolic Equation with a Nonlinear Boundary Condition cover
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Abstract

In this paper, a nonlinear parabolic equation of the form ut=(a(ux))xu_t = (a(u_x))_x for x(0,1),t>0,a(ux)=uxp2uxx \in (0, 1), t > 0, a(u_x) = |u_x|^{p–2}u_x if uxη>0,1<p<2u_x ≥ \eta > 0, 1 < p < 2, with nonlinear boundary condition a(uxr(1,t))=uq2u(l,t)a(u_x r(1, t)) = |u|^{q–2} u(l,t) is considered. It is proved that if qp3p+2>0qp - 3p + 2 > 0, then the solutions blow up in finite time. Moreover, estimates on the blowup profile (in xx) and the blowup rate (in tt) for x=1x = 1 are derived.

Cite this article

Michel Chipot, Ján Filo, An Example of Blowup for a Degenerate Parabolic Equation with a Nonlinear Boundary Condition. Z. Anal. Anwend. 17 (1998), no. 1, pp. 89–102

DOI 10.4171/ZAA/810