无界区域中的非线性双曲型方程

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On Nonlinear Hyperbolic Equation in Unbounded Domain

摘要: 本文研究无界区域中的非线性双曲方程u_tt+A²u+M(x,||A^1/2u||₂²)Au=0这类问题的模型来自梁的横向挠曲方程.本文利用不动点方法结合能量估计证明了当M与x有关时,上述方程局部解的存在唯一性.
- 非线性双曲型方程 /
- 无界区域 /
- 能量估计 /
- 不动点方法
Abstract: The following nonlinear hyperbolic equation is discussed in this paper:u_tt+A²u+M(x,||A^1/2u||₂²)Au=0, where A=-Δ+I and x∈Rⁿ. The model comes from the transverse deflection equation of an extensible beam. We prove that there exists a unique local solution of the above equation as M depends on x.
- nonlinear hyperbolic equations /
- unbounded domain /
- energy estimation /
- fixed point method

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