Abstract: We study the two-dimensional Cauchy problem for the quasilinear pseudo-parabolic equation with a regular nonlinear minor term endowed with periodic initial data and periodicity conditions. The minor term depends on a small parameter ε>0 and, as ε→0, converges weakly* to the expression incorporating the Dirac delta function, which models an instantaneous impulsive impact. We establish that the transition (shock) layer, associated with the Dirac delta function, is formed as ε→0, and that the family of strong solutions of the original problem converges to the strong solution of a two-scale microscopic-macroscopic model. This model consists of two equations and the set of initial and matching conditions, so that the `outer' macroscopic solution beyond the transition layer is governed by the quasilinear homogeneous pseudoparabolic equation at the macroscopic (`slow') timescale, while the transition layer solution is defined at the microscopic level and obeys the semilinear pseudoparabolic equation at the microscopic (`fast') timescale. The latter is derived based on the microstructure of the transition layer profile.

Cite: Kuznetsov I. , Sazhenkov S.
Strong solutions of impulsive pseudoparabolic equations
Nonlinear Analysis: Real World Applications. 2022. V.65. 103509 :1-19. DOI: 10.1016/j.nonrwa.2022.103509 WOS Scopus РИНЦ OpenAlex

Dates:

Submitted:	Dec 8, 2021
Accepted:	Jan 6, 2022

Identifiers:

Web of science:	WOS:000795544200007
Scopus:	2-s2.0-85123307899
Elibrary:	48145186
OpenAlex:	W4207037747

Citing:

DB	Citing
Scopus	5
OpenAlex	4
Web of science	5

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