Impulsive pseudo-parabolic equations with nonstandard growth, nonlinear source term and infinitesimal initial layer

Impulsive pseudo-parabolic equations with nonstandard growth, nonlinear source term and infinitesimal initial layer Научная публикация

Журнал

Journal of Elliptic and Parabolic Equations
ISSN: 2296-9020

Вых. Данные

Год: 2026, Номер: 1, Страницы: 1-24 Страниц : 24 DOI: 10.1007/s41808-025-00430-8

Ключевые слова

Pseudo-parabolic equation, Variable nonlinearity, Impulsive partial differential equation, Initial layer

Авторы

Antontsev Stanislav ¹ , Kuznetsov Ivan ^2,1 , Shmarev Sergey ³

Организации

1	Lavrentyev Institute of Hydrodynamics, Novosibirsk, Russian Federation
2	Altai State University, Barnaul, Russian Federation
3	Mathematics Department, University of Oviedo, Oviedo, Spain

We study a class of impulsive pseudo-parabolic equations with the nonlinear source terms depending on the solution, its gradient, and Laplacian. The smooth coefficient ϕn(t) before the source term has the support in [0, 1 n ] and converges to the Dirac delta function δ(t=0) as n → ∞. It is shown that the sequence of solutions of the non-instantaneous impulsive equations converges as n → ∞ to a solution of the instantaneous impulsive equation, and that the new initial datum is generated by the solution of a third-order equation on the infinitesimal initial layer.

Antontsev S. , Kuznetsov I. , Shmarev S.
Impulsive pseudo-parabolic equations with nonstandard growth, nonlinear source term and infinitesimal initial layer
Journal of Elliptic and Parabolic Equations. 2026. N1. P.1-24. DOI: 10.1007/s41808-025-00430-8

Поступила в редакцию:	7 авг. 2025 г.
Принята к публикации:	15 дек. 2025 г.
Опубликована в печати:	8 янв. 2026 г.

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