Impulsive limit in nonlinear mixed initial-boundary value problem for pseudo-parabolic equations with nonstandard growth

Impulsive limit in nonlinear mixed initial-boundary value problem for pseudo-parabolic equations with nonstandard growth Full article

Journal

Nonlinear Differential Equations and Applications NoDEA
ISSN: 1420-9004

Output data

Year: 2026, Volume: 33, Article number : 123, Pages count : 21 DOI: 10.1007/s00030-026-01249-5

Authors

Antontsev S. ¹ , Kuznetsov I. ^1,2,3 , Ozturk Yetkil E. ⁴ , Aitzhanov S. ^3,5

Affiliations

1	Lavrentyev Institute of Hydrodynamics
2	Altay State University, Barnaul, Russian Federation
3	Institute Mathematics and Mathematical Modeling, Almaty, Kazakhstan
4	Hacettepe University, Ankara, Turkiye
5	Al-Farabi Kazakh National University, Almaty, Kazakhstan

In the present paper, we study the nonlinear mixed initialboundary value problem for the pseudo-parabolic differential equation with p-Laplacian with a mixed boundary condition. The main novelty is that we study impulsive limit. This means that a fast reaction term is also multiplied by a characteristic function 1[0,1/n](t), i.e. the term n1[0,1/n](t) approximates the Dirac delta function δ(t=0). In order to pass to the limit as n →∞, we rescale the problem by the procedure t = nt : [0, 1n ] → [0, 1] on an infinitesimal initial layer, which also contains a rescaled mixed boundary condition. In the impulsive limit, we get the problem on infinitesimal initial layer giving a new initial data.

Antontsev S. , Kuznetsov I. , Ozturk Yetkil E. , Aitzhanov S.
Impulsive limit in nonlinear mixed initial-boundary value problem for pseudo-parabolic equations with nonstandard growth
Nonlinear Differential Equations and Applications NoDEA. 2026. Т.33. 123 :1-21. DOI: 10.1007/s00030-026-01249-5 OpenAlex

Submitted:	Feb 24, 2026
Accepted:	Jun 24, 2026
Published print:	Aug 25, 2026

≡ OpenAlex:

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