Nonexistence criteria for a generalized Boussinesq-type equation in bounded and unbounded domains

Abstract

In this paper, we consider a generalized Boussinesq-type equation posed in $ (0,\infty)\times \Omega $, where $ \Omega\subset \mathbb{R}^N $. The considered equation arises in many physical models including the description of nonstationary processes in crystalline semiconductors. We will handle two cases: $ \Omega = \overline{\mathbb{R}^N\backslash{B_1}} $ and $ \Omega = B_1\backslash\{0\} $, where $ B_1 $ is the closed unit ball in $ \mathbb{R}^N $. Using a unified approach, we establish nonexistence criteria for each case. Moreover, no restriction on the sign of solutions is imposed.