Bulletin of the Iranian Mathematical Society

Bulletin of the Iranian Mathematical Society

The geometric properties of a degenerate parabolic equation with periodic source term

Document Type : Research Paper

Authors
G. Guo 1
J. Q. Pan 2
1 Institute of Mathematics‎, ‎Shanghai Normal University‎, ‎Shanghai‎, ‎200235‎, ‎China and ‎Institute of Mathematics‎, ‎Jimei University‎, ‎Xiamen‎, ‎361021 China.
2 Institute of Mathematics‎, ‎Jimei University‎, ‎Xiamen‎, ‎361021 China.
Abstract
In this paper, we discuss the geometric properties of solution and lower bound estimate of ∆um−1 of the Cauchy problem for a degenerate parabolic equation with periodic source term ut =∆um+ upsint. Our objective is to show that: (1)with continuous variation of time t, the surface ϕ = [u(x,t)]mδq is a complete Riemannian manifold floating in space RN+1and is tangent to the space RN at ∂H0(t); (2)the surface u = u(x,t) is tangent to the hyperplane W(t) at ∂Hu(t).
Keywords
Degenerate parabolic equation
~Riemannian manifold
~Periodic source term
Subjects
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Bulletin of the Iranian Mathematical Society
Volume 42, Issue 4 - Serial Number 4
August 2016
Pages 799-808

  • Receive Date 22 July 2014
  • Revise Date 03 April 2015
  • Accept Date 04 April 2015