论文标题
关于半线性规律性损失类型$σ$进化模型的Cauchy问题带有内存项
On the Cauchy problem for semilinear regularity-loss-type $σ$-evolution models with memory term
论文作者
论文摘要
在本文中，我们考虑了具有指数衰减记忆项的半线性$σ$进化模型的凯奇问题。关于相应的线性库奇问题，我们得出了一些溶液和广义扩散现象的一些规律性损失型估计。特别是，获得的解决方案的估计比上一篇论文[20]中的估计更明确。然后，我们通过在某些空间维度中确定了半线性库奇问题的关键指数，即通过证明具有较低规律性订单的Sobolev解决方案的全局（及时）存在，即使对于任何分数值$ f note $σ\ geqslant 1 $。
In this paper, we consider the Cauchy problem for semilinear $σ$-evolution models with an exponential decay memory term. Concerning the corresponding linear Cauchy problem, we derive some regularity-loss-type estimates of solutions and generalized diffusion phenomena. Particularly, the obtained estimations for solutions are sharper than those in the previous paper [20]. Then, we determine the critical exponents for the semilinear Cauchy problem with power nonlinearity in some spatial dimensions by proving global (in time) existence of Sobolev solutions with low regularity of fractional orders and blow-up result for the Sobolev solutions even for any fractional value of $σ\geqslant 1$.
