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2010•Journal of Mathematical PhysicsRequires access

Optimal solution for the viscous nonlinear dispersive wave equation

Chunyu Shen, Anna Gao

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Abstract

In this paper, we study the optimal control problem for the viscous nonlinear dispersive wave equation. We first prove the existence and uniqueness of a weak solution to this equation in a short interval by using the Galerkin method. Furthermore, the existence of an optimal solution to the viscous nonlinear dispersive wave equation is proved.

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What this paper is about

In this paper, we study the optimal control problem for the viscous nonlinear dispersive wave equation. We first prove the existence and uniqueness of a weak solution to this equation in a short interval by using the Galerkin method. Furthermore, the existence of an optimal solution to the viscous nonlinear dispersive wave equation is proved.

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OpenAlex reports 2 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

In this paper, we study the optimal control problem for the viscous nonlinear dispersive wave equation. We first prove the existence and uniqueness of a weak solution to this equation in a short interval by using the Galerkin method. Furthermore, the existence of an optimal solution to the viscous nonlinear dispersive wave equation is proved.

Key concepts: Uniqueness, Mathematics, Mathematical analysis, Galerkin method, Dispersive partial differential equation, Nonlinear system, Wave equation, Burgers' equation

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