Moscow Mathematical Journal

Volume 26, Issue 3, July–September 2026 pp. 333–387.

Fujita-Type Existence and Nonexistence for an Inhomogeneous Weighted Nonlocal Noncoercive Parabolic Differential Inequality

Authors: Minhan Li (1) and Zhong Bo Fang (1)
Author institution:(1) School of Mathematical Sciences, Ocean University of China, Qingdao 266100, P.R. China

Summary:

This work is devoted to the investigation of existence and nonexistence of nontrivial nonnegative (or positive) weak solutions for an inhomogeneous weighted nonlocal noncoercive parabolic differential inequality in the whole space, in which the general weakly coercive operators involve weighted polytropic filtration operator or generalized mean curvature operator and the weight functions may be singular or degenerate at the origin. Based on the argument of the nonlinear parabolic capacity, we establish the new Fujita-type nonexistence results. Besides, we give some new conditions of Fujita-type existence.

2020 Math. Subj. Class. 35K59, 35R45, 35B33, 35B53.

Keywords: Inhomogeneous parabolic differential inequality, weighted nonlocal source, nonexistence, existence.

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