Impulsive pseudo-parabolic equation with nonlinear Robin boundary condition
Antontsev S. Kuznetsov I. Aitzhanov S.
October 2026Elsevier Ltd
Nonlinear Analysis: Real World Applications
2026#91
In the present paper, we study impulsive pseudo-parabolic equation with the nonlinear Robin boundary condition. In general, impulsive differential equations contain an approximation φ n (t) of the Dirac delta function depending on n∈N. The support of φ n (t) is the time interval [0, 1/ n]. In order to pass to the limit as n → ∞, we apply rescaling ϑ=tn:[0,1/n]↦[0,1] and get a new initial-boundary value problem on an infinitesimal initial layer ϑ ∈ [0, 1]. In the limit, this problem allows us to calculate new initial data, which implies that there is a gap in the limit solution at t=0. In the rest of the domain, outside of an infinitesimal initial layer, we apply shifting t˜:=t−1n and obtain an initial boundary value problem in the limit without a singular source term, but with a new initial data.
Impulsive differential equation , Pseudo-parabolic equation , Robin boundary condition
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Lavrentyev Institute of Hydrodynamics SB RAS, Novosibirsk, Russian Federation
Altai State University, Barnaul, Russian Federation
Institute of Mathematics and Mathematical Modelling, Almaty, Kazakhstan
Al-Farabi, Kazakh National University, Almaty, Kazakhstan
Lavrentyev Institute of Hydrodynamics SB RAS
Altai State University
Institute of Mathematics and Mathematical Modelling
Al-Farabi
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026