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Pure Mathematics 2023
具有记忆项的对数 Boussinesq型方程解的长时间行为研究
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Abstract:
本文考虑一类具有记忆项的对数梁方程的初边值问题。利用 Galerkin 方法结合对数 Sobolev 不等式及对数 Gronwall 不等式，我们证明了解的全局存在性。在此基础上，我们借助位势井思想进一步得到了系统在适当初值条件下的指数烹减及指数增长。
This paper is concerned with the initial value problem of a logarithmic beam equations
with memory. Using Galerkin method, logarithmic Sobolev inequality and the
Gronwall inequality, we obtain the global existence of the solutions. Moreover, we prove the exponential decay and exponential growth of the system by using potential
well theory.
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