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Stability of nonlinear impulsive partial differential equations

Qi Luo, Yutian Zhang

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Abstract

Stability of a class of nonlinear impulsive partial differential equations is discussed in this paper. The main idea is translating stability of the considered nonlinear impulsive partial differential equation into that of the corresponding linear impulsive ordinary differential equation via Gronwall-Bellman inequality with impulse on the basis of comparison theorem. Some theoretical criteria for stability of nonlinear impulsive partial differential equations are then given.

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What this paper is about

Stability of a class of nonlinear impulsive partial differential equations is discussed in this paper. The main idea is translating stability of the considered nonlinear impulsive partial differential equation into that of the corresponding linear impulsive ordinary differential equation via Gronwall-Bellman inequality with impulse on the basis of comparison theorem. Some theoretical criteria for stability of nonlinear impulsive partial differential equations are then given.

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Available abstract

Stability of a class of nonlinear impulsive partial differential equations is discussed in this paper. The main idea is translating stability of the considered nonlinear impulsive partial differential equation into that of the corresponding linear impulsive ordinary differential equation via Gronwall-Bellman inequality with impulse on the basis of comparison theorem. Some theoretical criteria for stability of nonlinear impulsive partial differential equations are then given.

Key concepts: Nonlinear system, Mathematics, Impulse (physics), First-order partial differential equation, Partial differential equation, Stochastic partial differential equation, Mathematical analysis, Differential equation

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