高维强阻尼非线性波动方程整体解的渐近理论

The Asymptotic Theory of Global Solutions for Strongly Damped Nonlinear Wave Equations in Higher-dimensions

采用整体迭代法,研究强阻尼非线性波动方程utt-Δu-μΔut=εf(t,x,Du;ε),(t>0,x∈Rn)Cauchy问题整体解的渐近理论,在Sobolev空间中,当空间维数n>2α)时,证明了初值问题的适定性α(1+1和形式近似解的合理性.

By using the global iterative technique, this paper studies the asymptotic theory of global solutions of Cauchy's problems for strongly damped nonlinear wave equations u_(tt)-Δu-μΔu_t=εf(t,x,Du;ε),(t>0,x∈R^n). In a suitable Sobolev space, with space dimension n>2α(1+1α), the wellposedness of the initial value problems and validity of formal approximations are demonstrated.