科研之友
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摘要
We study the nonlinear viscoelastic wave equation %26lt;br%26gt;u(tt) - k(0)Delta u + integral(t)(0) g(t - s)div[a(x)del u(s)]ds+(k(1) + b(x)vertical bar u(t)vertical bar(m-2))u(t) = vertical bar u vertical bar(p-2)u %26lt;br%26gt;with dissipative boundary conditions. Under some restrictions on the initial data and the relaxation function and without imposing any restrictive assumption on a(x), we show that the rate of decay is similar to that of g. We also prove the blow-up results for certain solutions in two cases. In the case k(1) = 0, m = 2, we show that the solutions blow up in finite time under some restrictions on initial data and for arbitrary initial energy. In another case, k(1) %26gt;= 0, m %26gt;= 2, we prove a nonexistence result when the initial energy is less than potential well depth.
- 出版日期2013-12
