In this paper we study the initial-boundary value problem of the multidimensional viscoelasticity equation with nonlinear source term u t t ? Δ u t ? ∑ i = 1 N ? ? x i σ i ( u x i ) = f ( u ) . By using the potential well method, we first prove the global existence. Then we prove that when time t → + ∞ , the solution decays to zero exponentially under some assumptions on nonlinear functions and the initial data.
展开▼
机译:在本文中,我们研究了非线性源术语U T T的多维粘弹性方程的初始边界值问题? Δut? σi= 1 n? ? xiσi(u x i)= f(u)。通过使用潜在的井方法,我们首先证明了全球存在。然后,我们证明了时间t→+∞,解决方案在非线性函数的一些假设和初始数据的某些假设下指数衰减为零。
展开▼