In this paper, we deal with a time-weighted parabolic system coupled via nonlocal sources.
Firstly, we give the critical Fujita exponent of solutions. Secondly, we propose the time …

We investigate a quasilinear parabolic inequality of Hardy-Hénon type with a time forcing
term ut− div A (x, u, D u)≥ t γ| x| σ uq, x∈ RN, t> 0, u (x, t)≥ 0, x∈ RN, t> 0, u (x, 0)= u 0 (x)≥ …

The purpose of this paper is to show the existence of type-I blow-up solutions for the time-
weighted parabolic Lane-Emden system on Riemannian models. We first prove a sufficient …

In this paper, we investigate a nonlinear free boundary problem incorporating with nontrivial
spatial and exponential temporal weighted source. To portray the asymptotic behavior of the …

We consider the parabolic problem u _ t-Δ u= F (t, u) ut-Δ u= F (t, u) in Ω * (0, T) Ω×(0, T) with
homogeneous Dirichlet boundary conditions. The nonlinear term is given by F (t, u)=(f_1 (t) …

This article discusses the existence of global and blow-up solutions for the semilinear heat
equation with a variable exponent. The equation is given by ut− Δ u= h (t) f (u) p (x) in Ω×(0 …

In this paper, we study the reaction–diffusion equations with variable coefficients in some
bounded domains. At least one of the components of solutions blows up for every initial data …

A necessary and sufficient condition for the existence or nonexistence of global solutions to
the following fractional reaction-diffusion equations ut= Δ α u+ ψ (t) f (u), in RN×(0,∞), u …

In this paper, we study the existence and nonexistence of the global solutions to nonlinear
reaction‐diffusion equations ut (x, t)= Δ u (x, t)+ ψ (t) f (u (x, t)),(x, t)∈ Ω×(0,∞), u (·, 0)= u 0 …

In this article, we consider the following double phase problem with singular term and
convolution term− Δ pu− Δ qu= λ u− γ+∫ Ω| u| q μ∗| x− y| μ dy| u| q μ∗− 2 u in Ω, u> 0 in Ω …