Uniqueness and grow-up rate of solutions for pseudo-parabolic equations in ${\mathbb{R}}^n$ with a sublinear source

Abstract

In this paper, we solve an open problem appeared in Cao et al. (2009) concerning the uniqueness of solutions for a sublinear pseudo-parabolic Cauchy problem. In the zero initial case, we obtain the class of all non-trivial global solutions, whereas, the uniqueness of global solutions is established when the initial condition is non-zero. A lower grow-up rate of solutions is also obtained.