This article concerns the Cauchy problem for the fractional semilinear pseudo-parabolic equation. Through the Green’s function method, we prove the pointwise convergence rate of the solution. Furthermore, using this precise pointwise structure, we introduce a Sobolev space condition with negative index on the initial data and give the nonlinear critical index for blowing up.

中文翻译：

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分数阶半线性伪抛物方程的解的适定性

本文涉及分数半线性伪抛物方程的柯西问题。通过格林函数方法，我们证明了解的逐点收敛速度。此外，使用这种精确的点状结构，我们在初始数据上引入了具有负索引的Sobolev空间条件，并给出了爆炸的非线性临界索引。