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1.
Results on finite-time blow-up of solutions to the nonlocal parabolic problem

are established. They extend some known results to higher dimensions.

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2.
We prove the global existence and blow-up of solutions of an initial boundary value problem for nonlinear nonlocal parabolic equation with nonlinear nonlocal boundary condition. Obtained results depend on the behavior of variable coefficients for large values of time.  相似文献   

3.
In this paper we study existence and uniqueness of solutions to some cases of the following nonlocal elliptic problem:
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4.
In this article, we investigate the blow-up properties of the positive solutions for a doubly degenerate parabolic equation with nonlocal source and nonlocal boundary condition. The conditions on the existence and nonexistence of global positive solutions are given. Moreover, we give the precise blow-up rate estimate and the uniform blow-up estimate for the blow-up solution.  相似文献   

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This paper deals with a semi-linear parabolic system with nonlinear nonlocal sources and nonlocal boundaries.By using super-and sub-solution techniques,we first give the sufficient conditions that the classical solution exists globally and blows up in a finite time respectively,and then give the necessary and sufficient conditions that two components u and v blow up simultaneously.Finally,the uniform blow-up profiles in the interior are presented.  相似文献   

7.
In this paper, we investigate the positive solution of nonlinear degenerate equation with Dirichlet boundary condition. The blow-up criteria is obtained. Furthermore, we prove that under certain conditions, the solutions have global blow-up. When f(u)=up,0<p1, we gained blow-up rate estimate.  相似文献   

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9.
Conditions for the existence and uniqueness of weak solutions for a class of nonlinear nonlocal degenerate parabolic equations are established. The asymptotic behaviour of the solutions as time tends to infinity are also studied. In particular, the finite time extinction and polynomial decay properties are proved.  相似文献   

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In this paper, we study the existence, uniqueness, multiplicity, and stability of positive solution of a nonlinear elliptic problem that combines local and nonlocal terms, taking the form of an integral in the space. The proofs are mainly based on fixed point theorems, bifurcation techniques, sub‐supersolutions, and continuation arguments. Copyright © 2012 John Wiley & Sons, Ltd.  相似文献   

12.
We consider the nonlocal diffusion equation


on the space interval , with Dirichlet boundary conditions. It is known that if the curve remains in a compact subset of for all times, then blow-up cannot occur in infinite time. The aim of this paper is to show that the assumption on is sharp: for a large class of functions approaching the boundary as , blow-up in infinite time does occur for certain initial data. Moreover, the asymptotic behavior of the corresponding solution is precisely estimated and more general nonlinearities are also considered.

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13.
L.E. Payne 《Applicable analysis》2013,92(12):2245-2256
The goal of this article is the determination of upper and lower bounds for the blow-up time t for a class of non-linear parabolic problems with time dependent coefficients under Robin type boundary conditions.  相似文献   

14.
15.
We show the existence of solution for some classes of nonlocal problems. Our proof combines the presence of sub and supersolution with the pseudomonotone operators theory.  相似文献   

16.
We use the priori estimate method to prove the existence and uniqueness of a solution as well as its dependence on the given data of a singular time fractional mixed problem having a memory term. The considered fractional equation is associated with a nonlocal condition of integral type and a Neuman condition. Our results develop and show the efficiency and effectiveness of the energy inequalities method for the time fractional order differential equations with a nonlocal condition.  相似文献   

17.
This paper deals with propagations of singularities in solutions to a parabolic system coupled with nonlocal nonlinear sources. The estimates for the four possible blow-up rates as well as the boundary layer profiles are established. The critical exponent of the system is determined also. This work was supported by the National Natural Science Foundation of China (Grant No. 10771024)  相似文献   

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This paper concerns with a nonlinear degenerate parabolic system coupled via nonlocal sources, subjecting to homogeneous Dirichlet boundary condition. The main aim of this paper is to study conditions on the global existence and/or blow-up in finite time of solutions, and give the estimates of blow-up rates of blow-up solutions.  相似文献   

20.
We study the existence, uniqueness and continuous dependence on initial data of the solution for a nonlocal Cahn-Hilliard equation with Dirichlet boundary condition on a bounded domain. Under a nondegeneracy assumption the solutions are classical but when this is relaxed, the equation is satisfied in a weak sense. Also we prove that there exists a global attractor in some metric space.  相似文献   

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