论文标题
与时间相关系数的四阶抛物线系统解决方案的行为
Behaviour in time of solutions to fourth-order parabolic systems with time dependent coefficients
论文作者
论文摘要
本文介绍了在有限域中$ω\ subset \ mathbb {r}^n，n \ geq 2 $中的非线性第四阶抛物线系统的初始数值问题。在源条款上引入适当的条件，我们获得了一个时间间隔$ [0，t]，$，该解决方案通过得出$ t^*$的下限$ t $而保持界限。此外，我们在空间域的形状上建立了条件和足以保证解决方案在有限的时间$ t^*$中炸毁的数据，从而为$ t^*$得出了上限。
This paper deals with a class of initial-boundary value problems for nonlinear fourth order parabolic systems with time dependent coefficients in a bounded domain $Ω\subset \mathbb{R}^N, N\geq 2$. Introducing suitable conditions on the source terms, we obtain a time interval $[0,T],$ where the solution remains bounded by deriving a lower bound $T$ of $t^*$. Moreover, we establish conditions on the shape of the spatial domain and on data sufficient to guarantee that the solution blows up in finite time $t^*$, deriving an upper bound for $t^*$.
