Asymptotic Behavior for a Class of Logarithmic Wave Equations with Linear Damping

作者：Hu, Qingying; Zhang, Hongwei^*; Liu, Gongwei

来源：Applied Mathematics and Optimization, 2019, 79(1): 131-144.

DOI：10.1007/s00245-017-9423-3

• Logarithmic wave equation
• Initial boundary value problem
• Exponential growth
• Energy decay

We consider the initial boundary value problem for a class of logarithmic wave equations with linear damping. By constructing apotential well and using the logarithmic Sobolev inequality, we prove that, if the solution lies in the unstable set or the initial energy is negative, the solution will grow as an exponential function in the H01() norm as time goes to infinity. If the solution lies in a smaller set compared with the stable set, we can estimate the decay rate of the energy. These results are extensions of earlier results.

• 出版日期2019-2
• 单位河南工业大学