In [] Fujita showed that for positive solutions, the initial value problem (in RN) for ut= Δu+ up
with p> 1 exhibited the following behavior: If p< pc≡ 1+ 2/N, then the initial value problem …

We present new blow-up results for reaction-diffusion equations with nonlocal nonlinearities.
The nonlocal source terms we consider are of several types, and are relevant to various …

In this paper, we introduce a new method for investigating the rate and profile of blow-up of
solutions of diffusion equations with nonlocal nonlinear reaction terms. For large classes of …

The subject of blow-up in a finite time, or at least very rapid growth, of a solution to a partial
differential equation has been an area of intense re search activity in mathematics. Some …

A general approach to critical Fujita exponents in nonlinear parabolic problems - ScienceDirect
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We establish local existence and comparison for a model problem which incorporates the
effects of non‐linear diffusion, convection and reaction. The reaction term to be considered …

A nonlocal eigenvalue problem of the form u ″+ a (x) u+ Bu= λu with homogeneous
Dirichlet boundary conditions is considered, where B is a rank-one bounded linear operator …

In this paper, we consider a semilinear heat equation ut= Δu+ c (x, t) up for (x, t)∈ Ω×(0,∞)
with nonlinear and nonlocal boundary condition u|∂ Ω×(0,∞)=∫ Ωk (x, y, t) uldy and …

This paper investigates the blow-up and global existence of nonnegative solutions of the
system [Formula: see text] with homogeneous Dirichlet boundary data, where Ω⊂ RN is a …

In this paper, we study an evolution problem arises in the study of MEMS (micro-electro
mechanical system) device. We consider both parabolic and hyperbolic type problems. We …