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Issue: Tập 23, Số 7 (2026)
Section: Articles
DOI: 10.54607/hcmue.js.23.7.5705(2026)
Date Published: 27/07/2026
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Nguyen, T. L., & Nguyen, X. V. T. (2026). BLOW-UP OF SOLUTIONS TO A STOCHASTIC VISCOELASTIC EQUATION WITH LOGARITHMIC NONLINEARITY. Ho Chi Minh City University of Education Journal of Science, 23(7), 1628-1639. https://doi.org/10.54607/hcmue.js.23.7.5705(2026)

BLOW-UP OF SOLUTIONS TO A STOCHASTIC VISCOELASTIC EQUATION WITH LOGARITHMIC NONLINEARITY

Nguyen Thanh Long1,2, Nguyen Xuan Viet Trung1,2,3,
1 FPT University, Vietnam
2 FPT PolySchool Ho Chi Minh, Vietnam
3 Ho Chi Minh University of Education, Vietnam

Main Article Content

Abstract

This paper investigates qualitative properties of solutions, with particular emphasis on finite-time blow-up for a class of stochastic viscoelastic wave equations on a bounded domain. The model includes a viscoelastic term, a Kirchhoff-type term, and a logarithmic source term, thereby providing a framework that integrates nonlocal effects with random environmental noise. We construct an appropriate energy functional and apply Itô's formula to establish key technical lemmas and differential inequalities. Using the energy method together with auxiliary inequalities and Sobolev embedding theorems, we estimate the growth of the energy functional and prove finite-time blow-up. The main result establishes sufficient conditions on the initial data and system parameters guaranteeing finite-time blow-up, extending existing literature on stochastic wave equations and offering a theoretical basis for analyzing similar models in the future.

Keywords

partial differential equations, stochastic, blow-up, viscoelastic term, logarithmic nonlinearity, Kirchhoff equation

Article Details

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