共查询到20条相似文献,搜索用时 31 毫秒
1.
This paper considers a heat system with localized sources and local couplings subject to null Dirichlet boundary conditions,
for which both total and single point blow-up are possible. The aim of the paper is to identify the total and single point
blow-up via a complete classification for all the nonlinear parameters in the model. As preliminaries of the paper, simultaneous
versus non-simultaneous blow-up of solutions is involved, too. The results are then compared with those for another kind of
heat system coupled via localized sources in a previous paper of the authors. 相似文献
2.
Xianfa Song Sining Zheng Zhaoxin Jiang 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2005,50(4):1-10
This paper deals with a nonlinear diffusion system coupled via nonlinear reaction terms of power type. As results of interactions among the multi-nonlinearities in the system described by six exponents, global boundedness and blow-up criteria of positive solutions are determined. 相似文献
3.
This paper investigates the finite time blow-up of nonnegative solutions for a nonlinear diffusion system with a more complicated source term,which is a product of localized source,local source,and weight function,and complemented by homogeneous Dirichlet boundary conditions.The criteria are proposed to identify simultaneous and nonsimultaneous blow-up solutions.Moreover,the related classification for the four parameters in the model is optimal and complete.The results extend those in Zhang and Yang [12]. 相似文献
4.
This paper considers the finite time blow-up of nonnegative solutions for a nonlinear diffusion system with a more complicated source term, which is a product of localized source, local source, weight function, and complemented by homogeneous Dirichlet boundary conditions. It is proved that there exists initial data such that simultaneous or non-simultaneous blow-up occur. Moreover, the related classifications for the four parameters in the model is optimal and complete. The results extend those in Zhang and Yang (J. Appl. Math. Comput. 32:429?C441, 2010). 相似文献
5.
This paper deals with asymptotic behavior of solutions to a heat system with absorptions and coupling positive multi-nonlinearities. It is known that although absorption mechanisms may affect such as blow-up criteria, blow-up time, and initial data required for blow-up solutions, they cannot change blow-up rates of solutions in general. It has been reported in the current literature that blow-up rates for scalar equations with absorptions are all absorption-independent. In a previous paper of the authors, four absorption-independent simultaneous blow-up rates were obtained already for the same problem under weak absorptions. The present paper will furthermore prove that if the absorptions are unbalanced in the model (i.e., the absorption is stronger for one component and weaker for another), then there are in addition eight possible absorption-related blow-up rates for the model, besides the four absorption-independent ones. This exposes a significant difference between scalar and coupled nonlinear parabolic equations with absorptions. 相似文献
6.
Xianfa Song Sining Zheng Zhaoxin Jiang 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2005,56(1):1-10
This paper deals with a nonlinear diffusion system coupled via nonlinear reaction terms of power type. As results of interactions among the multi-nonlinearities in the system described by six exponents, global boundedness and blow-up criteria of positive solutions are determined.Supported by the National Natural Science Foundation of China.Received: December 12, 2001; revised: May 6, December 3, 2002 相似文献
7.
Sining Zheng Bingchen Liu Fengjie Li 《Journal of Mathematical Analysis and Applications》2007,326(1):414-431
This paper deals with a parabolic system, cross-coupled via a nonlinear source and a nonlinear boundary flux. We get a necessary and sufficient condition for the existence of non-simultaneous blow-up. In particular, four different simultaneous blow-up rates are obtained in different regions of parameters, described by an introduced characteristic algebraic system. It is observed that different initial data may result in different simultaneous blow-up rates even in the same region of parameters. 相似文献
8.
This paper deals with blow-up solutions in parabolic equations coupled via nonlocal nonlinearities, subject to homogeneous Dirichlet conditions. Firstly, some criteria on non-simultaneous and simultaneous blow-up are given, including four kinds of phenomena: (i) the existence of non-simultaneous blow-up; (ii) the coexistence of non-simultaneous and simultaneous blow-up; (iii) any blow-up must be simultaneous; (iv) any blow-up must be non-simultaneous. Next, total versus single point blow-up are classified completely. Moreover, blow-up rates are obtained for both non-simultaneous and simultaneous blow-up solutions. 相似文献
9.
This paper deals with parabolic equations with different diffusion coefficients and coupled nonlinear sources, subject to homogeneous Dirichlet boundary conditions. We give many results about blow-up solutions, including blow-up time estimates for all of the spatial dimensions, the critical non-simultaneous blow-up exponents, uniform blow-up profiles, blow-up sets, and boundary layer with or without standard conditions on nonlocal sources. The conditions are much weaker than the ones for the corresponding results in the previous papers. 相似文献
10.
Cristina Brändle Fernando Quirós Julio D. Rossi 《Journal of Mathematical Analysis and Applications》2005,308(1):92-104
We study a parabolic system of two non-linear reaction-diffusion equations completely coupled through source terms and with power-like diffusivity. Under adequate hypotheses on the initial data, we prove that non-simultaneous blow-up is sometimes possible; i.e., one of the components blows up while the other remains bounded. The conditions for non-simultaneous blow-up rely strongly on the diffusivity parameters and significant differences appear between the fast-diffusion and the porous medium case. Surprisingly, flat (homogeneous in space) solutions are not always a good guide to determine whether non-simultaneous blow-up is possible. 相似文献
11.
This paper deals with the blow-up behavior of radial solutions to a parabolic system multi-coupled via inner sources and boundary flux. We first obtain a necessary and sufficient condition for the existence of non-simultaneous blow-up, and then find five regions of exponent parameters where both non-simultaneous and simultaneous blow-up may happen. In particular, nine simultaneous blow-up rates are established for different regions of parameters. It is interesting to observe that different initial data may lead to different simultaneous blow-up rates even with the same exponent parameters. 相似文献
12.
We study numerical approximations to solutions of a system of two nonlinear diffusion equations in a bounded interval, coupled
at the boundary in a nonlinear way. In certain cases the system develops a blow-up singularity in finite time. Fixed mesh
methods are not well suited to approximate the problem near the singularity. As an alternative to reproduce the behaviour
of the continuous solution, we present an adaptive in space procedure. The scheme recovers the conditions for blow-up and
non-simultaneous blow-up. It also gives the correct non-simultaneous blow-up rate and set. Moreover, the numerical simultaneous
blow-up rates coincide with the continuous ones in the cases when the latter are known. Finally, we present numerical experiments
that illustrate the behaviour of the adaptive method. 相似文献
13.
Fengjie Li Bingchen Liu Sining Zheng 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2007,58(5):717-735
This paper deals with simultaneous and non-simultaneous blow-up for heat equations coupled via nonlinear boundary fluxes
. It is proved that, if m < q + 1 and n < p + 1, then blow-up must be simultaneous, and that, for radially symmetric and nondecreasing in time solutions, non-simultaneous
blow-up occurs for some initial data if and only if m > q + 1 or n > p + 1. We find three regions: (i) q + 1 < m < p/(p + 1 − n) and n < p+1, (ii) p + 1 < n < q/(q + 1 − m) and m < q+1, (iii) m > q+1 and n > p+1, where both simultaneous and non-simultaneous blow-up are possible. Four different simultaneous blow-up rates are obtained
under different conditions. It is interesting that different initial data may lead to different simultaneous blow-up rates
even for the same values of the exponent parameters.
Supported by the National Natural Science Foundation of China. 相似文献
14.
This paper deals with heat equations coupled via exponential and power nonlinearities, subject to null Dirichlet boundary conditions. The complete and optimal classification on non-simultaneous and simultaneous blow-ups is proposed by four sufficient and necessary conditions. We find out that, in some exponent region, the blow-up properties of the solutions depend much on the choosing of initial data. Moreover, all kinds of non-simultaneous and simultaneous blow-up rates are obtained. 相似文献
15.
Zhihua Dong 《Applicable analysis》2018,97(5):825-841
This paper deals with a parabolic system with different diffusion coefficients and coupled nonlocal sources, subject to homogeneous Dirichlet boundary conditions. The conditions on global existence, simultaneous or non-simultaneous blow-up, blow-up set, uniform blow-up profiles and boundary layer are got using comparison principle and asymptotic analysis methods. 相似文献
16.
This paper deals with asymptotic analysis of a parabolic system with inner absorptions and coupled nonlinear boundary fluxes.
Three simultaneous blow-up rates are established under different dominations of nonlinearities, and simply represented in
a characteristic algebraic system introduced for the problem. In particular, it is observed that two of the multiple blow-up
rates are absorption-related. This is substantially different from those for nonlinear parabolic problems with absorptions
in all the previous literature, where the blow-up rates were known as absorptionindependent. The results of the paper rely
on the scaling method with a complete classification for the nonlinear parameters of the model. The first example of absorption-related
blow-up rates was recently proposed by the authors for a coupled parabolic system with mixed type nonlinearities. The present
paper shows that the newly observed phenomena of absorptionrelated blow-up rates should be due to the coupling mechanism,
rather than the mixed type nonlinearities.
相似文献
17.
Zhongping Li Chunlai Mu Wanjuan Du 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2013,64(2):253-263
This paper deals with coupled nonlinear diffusion equations with absorptions. We characterize the range of parameters for which non-simultaneous blow up occurs. We establish the necessary and sufficient conditions for the occurrence of non-simultaneous blow up with proper initial data. Moreover, we obtain the optimal condition under which any blow up is non-simultaneous. 相似文献
18.
ABSTRACT This paper deals with blow-up and quenching solutions of degenerate parabolic problem involving m-Laplacian operator and nonlinear boundary flux. The blow-up and quenching criteria are classified under the conditions on the initial data but with less conditions on the relationship among the exponents, respectively. Moreover, asymptotic properties including singular rates, set and time estimates are determined for the blow-up solutions and the quenching solutions, respectively. 相似文献
19.
This work deals with heat equations coupled via nonlinear boundary flux which obey different laws. We give a complete classification for non-simultaneous and simultaneous blow-up by covering all of the possible exponents. 相似文献
20.
Bingchen Liu 《Applicable analysis》2013,92(10):1615-1627
This article deals with blow-up solutions in reaction–diffusion equations coupled via localized exponential sources, subject to null Dirichlet conditions. The optimal and complete classification is obtained for simultaneous and non-simultaneous blow-up solutions. Moreover, blow-up rates and blow-up sets are also discussed. It is interesting that, in some exponent regions, blow-up phenomena depend sensitively on the choosing of initial data, and the localized nonlinearities play important roles in the blow-up properties of solutions. 相似文献