Oscillation of damped second order quasilinear wave equations with mixed arguments
Ying Sui, Huimin Yu
TL;DR
This paper studies how damping influences the oscillation behavior of smooth solutions to certain quasilinear wave equations with mixed boundary conditions, providing conditions under which oscillation is suppressed.
Contribution
It introduces new sufficient conditions using Riccati transformation and inequalities to determine oscillation behavior in damped quasilinear wave equations.
Findings
Positive damping can prevent oscillation of solutions.
Sufficient conditions for oscillation are established.
Examples confirm the theoretical results.
Abstract
Following the previous work [1], we investigate the impact of damping on the oscillation of smooth solutions to some kind of quasilinear wave equations with Robin and Dirichlet boundary condition. By using generalized Riccati transformation and technical inequality method, we give some sufficient conditions to guarantee the oscillation of all smooth solutions. From the results, we conclude that positive damping can ``hold back" oscillation. At last, some examples are presented to confirm our main results.
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Taxonomy
TopicsDifferential Equations and Numerical Methods · Stability and Controllability of Differential Equations · Nonlinear Differential Equations Analysis