Global solvability for semi-discrete Kirchhoff equation
Fumihiko Hirosawa
TL;DR
This paper investigates the conditions under which the semi-discrete Kirchhoff wave equation has solutions that exist for all time and conserves energy, focusing on the discretized model of the classical Kirchhoff equation.
Contribution
It establishes global solvability and energy conservation results for the semi-discrete nonlinear Kirchhoff wave equation, a discretized version of the continuous model.
Findings
Proved global existence of solutions.
Demonstrated energy conservation.
Analyzed the semi-discrete model's properties.
Abstract
In this paper, we consider the global solvability and energy conservation for initial value problem of nonlinear semi-discrete wave equation of Kirchhoff type, which is a discretized model of Kirchhoff equation.
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Taxonomy
TopicsStability and Controllability of Differential Equations · Advanced Mathematical Physics Problems