Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Harnack Estimate for Positive Solutions to a Nonlinear Equation Under Geometric Flow

  • Fasihi-Ramandi, Ghodratallah (Department of Pure Mathematics, Faculty of Science Imam Khomeini International University) ;
  • Azami, Shahroud (Department of Pure Mathematics, Faculty of Science Imam Khomeini International University)
  • Received : 2019.08.28
  • Accepted : 2020.08.18
  • Published : 2021.09.30
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Abstract

In the present paper, we obtain gradient estimates for positive solutions to the following nonlinear parabolic equation under general geometric flow on complete noncompact manifolds $$\frac{{\partial}u}{{\partial}t}={\Delta}u+a(x,t)u^p+b(x,t)u^q$$ where, 0 < p, q < 1 are real constants and a(x, t) and b(x, t) are functions which are C2 in the x-variable and C1 in the t-variable. We shall get an interesting Harnack inequality as an application.

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References

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