锥退化流形上粘弹性发展方程的爆破性质
Blow up property for viscoelastic evolution equations on manifolds with conical degeneration
摘要：
本文研究了由\[u_{tt} - Δ_{\mathbb{B}}u + \int_{0}^{t}g(t-τ)Δ_{\mathbb{B}}u(τ)dτ+ f(x)u_{t}|u_{t}|^{m-2} = h(x)|u|^{p-2}u , \hspace{1 cm} x\in int\mathbb{B}, t > 0,\]描述的具有强阻尼项和源项的非线性粘弹性发展方程，其中$\mathbb{B}$是拉伸流形.首先证明了问题{1.1}在锥索伯列夫空间$\mathcal{H}^{1,\frac{n}{2}}_{2,0}(\mathbb{B}),$中的解在有限时间内对$p > m$和正的初始能量允许爆破。然后，我们构造了一个下界的爆破时间在适当的假设下的数据。
英文摘要：
This paper is concerned with the study of the nonlinear viscoelastic evolution equation with strong damping and source terms, described by \[u_{tt} - Δ_{\mathbb{B}}u + \int_{0}^{t}g(t-τ)Δ_{\mathbb{B}}u(τ)dτ+ f(x)u_{t}|u_{t}|^{m-2} = h(x)|u|^{p-2}u , \hspace{1 cm} x\in int\mathbb{B}, t > 0,\] where $\mathbb{B}$ is a stretched manifold. First, we prove the solutions of problem {1.1} in cone Sobolev space $\mathcal{H}^{1,\frac{n}{2}}_{2,0}(\mathbb{B}),$ admit a blow up in finite time for $p > m$ and positive initial energy. Then, we construct a lower bound for obtained blow up time under appropriate assumptions on data.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
