Exponential attractor for degenerate parabolic equations with dynamic boundary conditions

Abstract

Abstract: Different from the classical boundary conditions, the dynamic boundary conditions present fundamental challenges in studying the long-time behavior of the system because of their unique coupling. For the non-autonomous degenerate parabolic equations with dynamic boundary conditions, the existence of the pullback exponential attractor in a bounded domain was studied. The Lipschitz continuity of the solution process within the absorbing sets was established using the energy method. The solution process was decomposed by orthogonal projection, and the compressibility of the solution process of the non-orthogonal parts within the absorbing sets was proved. According to the existence theorem of the pullback exponential attractor in Banach space, the existence of the exponential attractor of the equation was obtained.

Key words: dynamic boundary conditions, degenerate parabolic equation, pullback exponential attractors, non-autonomous

CLC Number:

O175.2

LI Xin, LIU Kong-yu, LIU Yang. Exponential attractor for degenerate parabolic equations with dynamic boundary conditions[J]. Journal of Lanzhou University of Technology, 2025, 51(4): 157-165.

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