What question did this study set out to answer?

This research aims to analyze the existence and stability of solutions to a viscoelastic Kirchhoff-type wave equation.

Local Existence and Blow-Up Analysis for a Damped Viscoelastic Kirchhoff-Type Equation with Logarithmic Power Source

View Full Paper

Ask AI

Bookmark

Authors

Investigation reveals local existence and unbounded blow-up in solutions for viscoelastic equations, indicating critical behavior.

This research aims to analyze the existence and stability of solutions to a viscoelastic Kirchhoff-type wave equation.
Considered initial-boundary value problem with homogeneous Dirichlet boundary conditions.
Established local existence and uniqueness using a Banach fixed-point argument.
Investigated conditions leading to finite-time blow-up of solutions.
Local existence and uniqueness of weak solutions were successfully established.
Solutions may experience unbounded growth in finite time under positive initial energy and compatibility conditions.

Begüm Çalışkan Desova (2026) studied this question.

View Full Paper

Ask AI

Bookmark