대한수학회지 (Journal of the Korean Mathematical Society)

  • 제52권6호
  • /
  • Pages.1149-1159
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  • 2015
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  • 0304-9914(pISSN)
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  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지
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UPPER SEMICONTINUITY OF PULLBACK ATTRACTORS FOR NON-AUTONOMOUS GENERALIZED 2D PARABOLIC EQUATIONS

  • PARK, JONG YEOUL (DEPARTMENT OF MATHEMATICS PUSAN NATIONAL UNIVERSITY) ;
  • PARK, SUN-HYE (CENTER FOR EDUCATION ACCREDITATION PUSAN NATIONAL UNIVERSITY)
  • 투고 : 2014.10.10
  • 발행 : 2015.11.01
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초록

This paper is concerned with a generalized 2D parabolic equation with a nonautonomous perturbation $$-{\Delta}u_t+{\alpha}^2{\Delta}^2u_t+{\mu}{\Delta}^2u+{\bigtriangledown}{\cdot}{\vec{F}}(u)+B(u,u)={\epsilon}g(x,t)$$. Under some proper assumptions on the external force term g, the upper semicontinuity of pullback attractors is proved. More precisely, it is shown that the pullback attractor $\{A_{\epsilon}(t)\}_{t{\epsilon}{\mathbb{R}}}$ of the equation with ${\epsilon}>0$ converges to the global attractor A of the equation with ${\epsilon}=0$.

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참고문헌

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