Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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PROPERTIES OF POSITIVE SOLUTIONS FOR A NONLOCAL REACTION-DIFFUSION EQUATION WITH NONLOCAL NONLINEAR BOUNDARY CONDITION

  • Mu, Chunlai (COLLEGE OF MATHEMATICS AND STATISTICS CHONGQING UNIVERSITY) ;
  • Liu, Dengming (COLLEGE OF MATHEMATICS AND STATISTICS CHONGQING UNIVERSITY) ;
  • Zhou, Shouming (COLLEGE OF MATHEMATICS AND STATISTICS CHONGQING UNIVERSITY)
  • Received : 2009.04.04
  • Published : 2010.11.01
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Abstract

In this paper, we study the properties of positive solutions for the reaction-diffusion equation $u_t$ = $\Delta_u+{\int}_\Omega u^pdx-ku^q$ in $\Omega\times(0,T)$ with nonlocal nonlinear boundary condition u (x, t) = ${\int}_{\Omega}f(x,y)u^l(y,t)dy$ $\partial\Omega\times(0,T)$ and nonnegative initial data $u_0$ (x), where p, q, k, l > 0. Some conditions for the existence and nonexistence of global positive solutions are given.

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References

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