Asymptotic behavior of impulsive parabolic problem with infinite-dimensional impulsive set

2025

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DOI 10.1515/gmj-2025-2017
Data confidence 70 medium
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Abstract

Abstract In the paper we consider semilinear parabolic equation with a nonlinear term ε ⁢ f ⁢ ( u ) {\varepsilon f(u)} , whose trajectories undergo impulsive perturbations when they meet the impulsive set M = { ∥ u ∥ = R } {M=\{\|u\|=R\}} . We prove that for sufficiently small ε this problem generates an impulsive dynamical system which possesses a compact uniform attractor in the phase space L 2 {L^{2}} .