대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제49권6호
  • /
  • Pages.1179-1192
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  • 2012
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  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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DOUBLY NONLINEAR PARABOLIC EQUATIONS INVOLVING p-LAPLACIAN OPERATORS VIA TIME-DISCRETIZATION METHOD

  • Shin, Kiyeon (Department of Mathematics Pusan National University) ;
  • Kang, Sujin (Department of Nanomaterials Engineering Pusan National University)
  • 투고 : 2009.07.13
  • 발행 : 2012.11.30
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초록

In this paper, we consider a doubly nonlinear parabolic partial differential equation $\frac{{\partial}{\beta}(u)}{{\partial}t}-{\Delta}_pu+f(x,t,u)=0$ in ${\Omega}{\times}[0,T]$, with Dirichlet boundary condition and initial data given. We prove the existence of a discrete approximate solution by means of the Rothe discretization in time method under some conditions on ${\beta}$, $f$ and $p$.

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참고문헌

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