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In this paper, we address the solution of a semilinear heat equation with variable reaction subject to Dirichlet boundary conditions and nonnegative initial datum. Under some assumptions, we show that...
This paper deals with the blow-up properties of the solution to the degenerate and singular parabolic system with nonlocal sources, absorptions and homogeneous Dirichlet boundary conditions. The exist...
Let (M,g) be a complete noncompact Riemannian manifold. In this note, we derive a local gradient estimate for positive solution to a simple nonlinear parabolic equation
Parabolic partial differential equation with nonlocal boundary conditions arise in modeling of various physical phenomena in areas such as chemical diffusion, thermoelasticity, heat conduction process...
Explosive instabilities in two uniform spatially discrete schemes for a semilinear parabolic equation in one space dimension are studied by intensive numerical simulations. We shows for both schemes t...
In this paper, the solutions of the one dimensional non-homogeneous parabolic equations with a variable coefficient are obtained by means of variational iteration method (VIM). The results reveal that...
We begin by describing the set E(L) of nonnegative equilibrium solutions to the motivating example, which consists of problem (P) with the special choice f(u) = u(1 − u)(u − a) and 0 < a <...
Based on a high order absolutely stable implicit scheme, we construct the alternating group explicit iterative method (AGEI) for four order parabolic equations. The method is verified to be convergent...
A class of alternating group explicit iterative method using the C-N scheme is derived for solving four order parabolic equations, and the analysis for convergency is given. In the end, the numerical ...
In this work we investigate finite–approximate controllability for a nonlocal parabolic problem defined in an bounded domain of RN. First, using a variational approach, we prove the controllability re...
The goal of this paper is to study the existence of weak periodic solutions for some quasilinear parabolic equations with data measures and critical growth nonlinearity with respect to the gradient. T...
This paper deals with the blow-up profiles of the nonnegative solutions to a degenerate reaction-diffusion system with nonlinear nonlocal sources involved in a product with local terms, subject to the...
In this paper, we give some results on the blow-up behaviors of the solution to the mixed problem for some higher nonlinear hyperbolic evolution equation in finite time .By introducing the ``blow-up f...
In this article we consider an inverse parabolic problem of linear heat equation with nonlinear boundary condition. We identify the temperature and the unknown radiation term from an overspecified con...

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