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 Full article

Journal

Journal of Elliptic and Parabolic Equations
ISSN: 2296-9020

Output data

Year: 2026, Number: 1, Pages: 1-24 Pages count : 24 DOI: 10.1007/s41808-025-00430-8

Tags

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

Authors

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

Affiliations

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

Submitted:	Aug 7, 2025
Accepted:	Dec 15, 2025
Published print:	Jan 8, 2026

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