In this paper,we establish the exponential stability of the one-dimensional Euler-Bernoulli beam equation with local viscosity.On the one hand,we demonstrate that the Euler-Bernoulli beam equation system is exponentia...In this paper,we establish the exponential stability of the one-dimensional Euler-Bernoulli beam equation with local viscosity.On the one hand,we demonstrate that the Euler-Bernoulli beam equation system is exponentially stable by employing the multiplier method,which relies on an appropriately constructed Lyapunov function.On the other hand,we discretize the Euler-Bernoulli beam equation system using the finite volume difference method.For the resulting semi-discrete system,we construct a discretized multiplier based on the discretized Lyapunov function.Finally,we prove that the semi-discrete Euler-Bernoulli beam equation system is also uniformly exponentially stable.展开更多
基金supported by the Natural Science Foundation of Beijing(No.1232006)。
文摘In this paper,we establish the exponential stability of the one-dimensional Euler-Bernoulli beam equation with local viscosity.On the one hand,we demonstrate that the Euler-Bernoulli beam equation system is exponentially stable by employing the multiplier method,which relies on an appropriately constructed Lyapunov function.On the other hand,we discretize the Euler-Bernoulli beam equation system using the finite volume difference method.For the resulting semi-discrete system,we construct a discretized multiplier based on the discretized Lyapunov function.Finally,we prove that the semi-discrete Euler-Bernoulli beam equation system is also uniformly exponentially stable.
