非线性p(x)-Kirchhoff方程在动态边界条件下的非全局存在性(英文)

考虑在动态边界条件下,非线性p(x)-Kirchhoff方程组解的非全局存在性,该方程组带有非线性外力项Q和非线性源项f.通过研究方程组解的自然能量,证明在初始能量小于一个临界值时,方程组解的非全局存在性.并将带有拟线性齐次p-拉普拉斯算子的p-Kirchhoff方程组推广到p(x)-Kirchhoff方程组,该方程组近年被用来模拟很多现象.

Global nonexistence for nonlinear p(x)-Kirchhoff systems with dynamic boundary conditions

This paper considered the global non-existence of solutions
of nonlinear $p(x)$-Kirchhoff systems with dynamic boundary
conditions, which involve nonlinear external damping terms $Q$ and
nonlinear driving forces $f$. Through the study of the natural
energy associated to the solutions $u$ of the systems, the
nonexistence of global solutions, when the initial energy is
controlled above by a critical value was proved. And the
$p$-Kirchhoff equations involving the quasilinear homogeneous
$p$-Laplace operator were extended to the $p(x)$-Kirchhoff equations
which have been used in the last decades to model various
phenomena.