# Moscow Mathematical Journal

Volume 24, Issue 3, July–September 2024 pp. 357–371.

The Absence of Global Weak Solutions for a Quasilinear Parabolic Differential Inequality in Exterior Domain

**Authors**:
Wentao Huo (1), Suping Xiao (2), and Zhong Bo Fang (3)

**Author institution:**(1) School of Mathematical Sciences, Ocean University of China, Qingdao 266100, P.R. China

(2) School of Mathematical and Computer Science, Shanxi Normal University, Taiyuan 03000, P.R. China

(3) School of Mathematical Sciences, Ocean University of China, Qingdao 266100, P.R. China

**Summary: **

This paper is concerned with the absence of nontrivial nonnegative global weak solutions for a quasilinear parabolic differential inequality in the higher dimensional space ($N\geq2$). Assuming that the non-homogeneous Dirichlet boundary condition relies on both time and space, we derive a criterion of the absence which depends on the effects of quasilinear diffusion and the behavior of time-varying coefficient precisely.

2020 Math. Subj. Class. 35B53, 35K59, 35K15.

**Keywords:**Quasilinear parabolic differential inequality, exterior problem, non-homogeneous Dirichlet boundary condition, nonexistence.

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