论文标题
全球存在和有限的时间爆炸，用于混合伪 - 羟基蛋白酶$ p $ -laplacian类型方程
Global existence and finite time blowup for a mixed pseudo-parabolic $p$-Laplacian type equation
论文作者
论文摘要
本文涉及混合伪 - 羟基蛋白酶$ P $ -Laplacian类型方程的初始价值问题。通过建造一个潜在的井家族，我们首先介绍了潜在孔深度的明确表达，然后证明了全球溶液的存在，独特性和衰减估计，以及具有亚临界初始能量的溶液的爆炸现象。接下来，我们将这些结果一致地扩展到关键的初始能量。最后，通过进一步分析$ω$ - 限制解决方案的属性，证明了具有超临界初始能量的全球解决方案的存在，独特性和渐近行为。
This paper concerns the initial-boundary value problem for a mixed pseudo-parabolic $p$-Laplacian type equation. By constructing a family of potential wells, we first present the explicit expression for the depth of potential well, and then prove the existence, uniqueness and decay estimate of global solutions and the blowup phenomena of solutions with subcritical initial energy. Next, we extend parallelly these results to the critical initial energy. Lastly, the existence, uniqueness and asymptotic behavior of global solutions with supercritical initial energy are proved by further analyzing the properties of $ω$-limits of solutions.
