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• W4386566196 abstract "We study the multi-dimensional initial-boundary value problem for the semilinear pseudoparabolic equation with a regular nonlinear minor term, which, in general, may be superlinear. This term models a non-instantaneous but a very rapid absorption with q(x)-growth. The minor term depends on a positive integer parameter n and, as n→+∞, converges weakly⋆ to the expression incorporating the Dirac delta function, which, in turn, models an instant absorption at the initial moment. We prove that an infinitesimal initial layer, associated with the Dirac delta function, is formed as n→+∞, and that the family of regular weak solutions to 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, boundary, and matching conditions, so that the ‘outer’ macroscopic solution beyond the initial layer is governed by the linear homogeneous pseudoparabolic equation at the macroscopic (‘slow’) timescale, while the initial layer solution is defined at the microscopic level and obeys the semilinear pseudoparabolic equation at the microscopic (‘fast’) timescale. The latter equation inherits the full information about the profile of the original non-instantaneous absorption. In general, the research is devoted to pseudoparabolic equations with measure data depending on an unknown solution." @default.
• W4386566196 created "2023-09-10" @default.
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• W4386566196 date "2024-02-01" @default.
• W4386566196 modified "2023-10-16" @default.
• W4386566196 title "Strong solutions of a semilinear impulsive pseudoparabolic equation with an infinitesimal initial layer" @default.
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• W4386566196 doi "https://doi.org/10.1016/j.jmaa.2023.127751" @default.
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