December  2007, 6(4): 1113-1129. doi: 10.3934/cpaa.2007.6.1113

Non-simultaneous blow-up for heat equations with positive-negative sources and coupled boundary flux

1. 

Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China, China

Received  October 2006 Revised  February 2007 Published  September 2007

This paper deals with non-simultaneous blow-up for heat equations with positive-negative sources coupled via nonlinear boundary flux. At first, we establish the necessary-sufficient conditions for non-simultaneous blow-up of solutions under suitable initial data. Furthermore, the sufficient conditions are determined under which any blow-up of solutions to the model would be non-simultaneous. Comparing with those for a similar system possessing negative-negative sources obtained in a previous paper [19] we show clearly the contribution of the positive source in the present model to the non-simultaneous blowing up behavior of solutions.
Citation: Lan Qiao, Sining Zheng. Non-simultaneous blow-up for heat equations with positive-negative sources and coupled boundary flux. Communications on Pure and Applied Analysis, 2007, 6 (4) : 1113-1129. doi: 10.3934/cpaa.2007.6.1113
[1]

C. Brändle, F. Quirós, Julio D. Rossi. Non-simultaneous blow-up for a quasilinear parabolic system with reaction at the boundary. Communications on Pure and Applied Analysis, 2005, 4 (3) : 523-536. doi: 10.3934/cpaa.2005.4.523

[2]

Nadjat Doudi, Salah Boulaaras, Nadia Mezouar, Rashid Jan. Global existence, general decay and blow-up for a nonlinear wave equation with logarithmic source term and fractional boundary dissipation. Discrete and Continuous Dynamical Systems - S, 2022  doi: 10.3934/dcdss.2022106

[3]

Hong Yi, Chunlai Mu, Guangyu Xu, Pan Dai. A blow-up result for the chemotaxis system with nonlinear signal production and logistic source. Discrete and Continuous Dynamical Systems - B, 2021, 26 (5) : 2537-2559. doi: 10.3934/dcdsb.2020194

[4]

Gongwei Liu. The existence, general decay and blow-up for a plate equation with nonlinear damping and a logarithmic source term. Electronic Research Archive, 2020, 28 (1) : 263-289. doi: 10.3934/era.2020016

[5]

Jinxing Liu, Xiongrui Wang, Jun Zhou, Huan Zhang. Blow-up phenomena for the sixth-order Boussinesq equation with fourth-order dispersion term and nonlinear source. Discrete and Continuous Dynamical Systems - S, 2021, 14 (12) : 4321-4335. doi: 10.3934/dcdss.2021108

[6]

Yuya Tanaka, Tomomi Yokota. Finite-time blow-up in a quasilinear degenerate parabolic–elliptic chemotaxis system with logistic source and nonlinear production. Discrete and Continuous Dynamical Systems - B, 2022  doi: 10.3934/dcdsb.2022075

[7]

Zhiqing Liu, Zhong Bo Fang. Blow-up phenomena for a nonlocal quasilinear parabolic equation with time-dependent coefficients under nonlinear boundary flux. Discrete and Continuous Dynamical Systems - B, 2016, 21 (10) : 3619-3635. doi: 10.3934/dcdsb.2016113

[8]

Claudianor O. Alves, M. M. Cavalcanti, Valeria N. Domingos Cavalcanti, Mohammad A. Rammaha, Daniel Toundykov. On existence, uniform decay rates and blow up for solutions of systems of nonlinear wave equations with damping and source terms. Discrete and Continuous Dynamical Systems - S, 2009, 2 (3) : 583-608. doi: 10.3934/dcdss.2009.2.583

[9]

Bouthaina Abdelhedi, Hatem Zaag. Single point blow-up and final profile for a perturbed nonlinear heat equation with a gradient and a non-local term. Discrete and Continuous Dynamical Systems - S, 2021, 14 (8) : 2607-2623. doi: 10.3934/dcdss.2021032

[10]

Alexander Gladkov. Blow-up problem for semilinear heat equation with nonlinear nonlocal Neumann boundary condition. Communications on Pure and Applied Analysis, 2017, 16 (6) : 2053-2068. doi: 10.3934/cpaa.2017101

[11]

Frank Merle, Hatem Zaag. O.D.E. type behavior of blow-up solutions of nonlinear heat equations. Discrete and Continuous Dynamical Systems, 2002, 8 (2) : 435-450. doi: 10.3934/dcds.2002.8.435

[12]

Keng Deng, Zhihua Dong. Blow-up for the heat equation with a general memory boundary condition. Communications on Pure and Applied Analysis, 2012, 11 (5) : 2147-2156. doi: 10.3934/cpaa.2012.11.2147

[13]

Jorge A. Esquivel-Avila. Blow-up in damped abstract nonlinear equations. Electronic Research Archive, 2020, 28 (1) : 347-367. doi: 10.3934/era.2020020

[14]

Victor A. Galaktionov, Juan-Luis Vázquez. The problem Of blow-up in nonlinear parabolic equations. Discrete and Continuous Dynamical Systems, 2002, 8 (2) : 399-433. doi: 10.3934/dcds.2002.8.399

[15]

Van Tien Nguyen. On the blow-up results for a class of strongly perturbed semilinear heat equations. Discrete and Continuous Dynamical Systems, 2015, 35 (8) : 3585-3626. doi: 10.3934/dcds.2015.35.3585

[16]

Pan Zheng, Chunlai Mu, Xuegang Hu. Boundedness and blow-up for a chemotaxis system with generalized volume-filling effect and logistic source. Discrete and Continuous Dynamical Systems, 2015, 35 (5) : 2299-2323. doi: 10.3934/dcds.2015.35.2299

[17]

Vo Anh Khoa, Le Thi Phuong Ngoc, Nguyen Thanh Long. Existence, blow-up and exponential decay of solutions for a porous-elastic system with damping and source terms. Evolution Equations and Control Theory, 2019, 8 (2) : 359-395. doi: 10.3934/eect.2019019

[18]

Nguyen Thanh Long, Hoang Hai Ha, Le Thi Phuong Ngoc, Nguyen Anh Triet. Existence, blow-up and exponential decay estimates for a system of nonlinear viscoelastic wave equations with nonlinear boundary conditions. Communications on Pure and Applied Analysis, 2020, 19 (1) : 455-492. doi: 10.3934/cpaa.2020023

[19]

Mingyou Zhang, Qingsong Zhao, Yu Liu, Wenke Li. Finite time blow-up and global existence of solutions for semilinear parabolic equations with nonlinear dynamical boundary condition. Electronic Research Archive, 2020, 28 (1) : 369-381. doi: 10.3934/era.2020021

[20]

Jong-Shenq Guo. Blow-up behavior for a quasilinear parabolic equation with nonlinear boundary condition. Discrete and Continuous Dynamical Systems, 2007, 18 (1) : 71-84. doi: 10.3934/dcds.2007.18.71

2020 Impact Factor: 1.916

Metrics

  • PDF downloads (61)
  • HTML views (0)
  • Cited by (2)

Other articles
by authors

[Back to Top]