Blow-up analysis for a reaction–diffusion equation with weighted nonlocal inner absorptions under nonlinear boundary flux

Ma, Lingwei; Fang, Zhong Bo

doi:10.1016/j.nonrwa.2016.05.005

Cited by 23 publications

(5 citation statements)

References 24 publications

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“…The existence and nonexistence of global solutions, bounds for blow-up time, blow-up rate, blow-up sets and asymptotic behavior for this type of equations were investigated by many authors. We refer the reader to see [14,15,24] and papers cited therein. For example, Song and Lv [14,24] studied the initial boundary value problem for the above equations with nonlinear Neumann boundary condition, and they derived the upper and lower bounds for blow-up time in three dimensional space [14].…”

Section: Introductionmentioning

confidence: 99%

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Some Results on Blow-up Phenomenon for Nonlinear Porous Medium Equations with Weighted Source

Chen²,

Song³

2020

Eur. J. Pure Appl. Math.

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This paper deals with the blow-up phenomena for a type of nonlinear porous medium equations with weighted source ut −4um = a(x)f(u) subject to Dirichlet (or Neumann) boundary conditions. Based on the auxiliary functions and differential-integral inequalities, the blow-up criterions which ensure that u cannot exist all time are given under two different assumptions, and the corresponding estimates on the upper bounds for blow-up time and blow-up rate are derived respectively. Moreover, we use three different methods to determine the lower bounds for blow-up time and blow-up rate estimates if blow-up does occurs.

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Section: Introductionmentioning

confidence: 99%

“…In [24], they further investigated the estimates of blow-up rate and the bounds for blow-up time in higher dimensional space. Ma and Fang [15] changed the diffusion term u into N i,j=1 a i,j (x)u x i x j in Eq. (1.6), where the upper and lower bounds for the blow-up time were derived in higher dimensional space.…”

Section: Introductionmentioning

confidence: 99%

Some Results on Blow-up Phenomenon for Nonlinear Porous Medium Equations with Weighted Source

Chen²,

Song³

2020

Eur. J. Pure Appl. Math.

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“…Thereinto, nonlinear reaction diffusion model plays an important role in the fields of physics, chemistry, biology and engineering, etc, as its global and blow-up solutions always reflect the stability and instability of heat and mass transport process. In the past decades, the study of reaction diffusion model gradually become hot issues for many mathematicians, see, for example, other studies [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] and the reference therein. Especially, for the Dirichlet boundary value problems, many authors have already focused on studying the existence of global and blow-up solutions, blow-up time, blow-up rate, and blow-up set.…”

Section: Introductionmentioning

confidence: 99%

Global and blow‐up analysis for a class of nonlinear reaction diffusion model with Dirichlet boundary conditions

Zhang

Wang

2018

Math Methods in App Sciences

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The work is concerned with the following nonlinear reaction diffusion model with Dirichlet boundary conditions: false(gfalse(ufalse)false)t=∇·false(ρfalse(false|∇u|pfalse)false|∇u|p−2∇ufalse)+hfalse(xfalse)kfalse(tfalse)ffalse(ufalse),in1emD×false(0,t∗false),ufalse(x,tfalse)=0,on1em∂D×false(0,t∗false),ufalse(x,0false)=u0false(xfalse)≥0,in1emtrueD¯, where p ≥ 2 is a real number and D⊂RNfalse(N≥2false) is a bounded domain with smooth boundary ∂D. Under some appropriate assumptions on the functions f,h,k,g,ρ, and initial value u0, by defining auxiliary functions and using a first‐order differential inequality technique, we not only present that the solution exists globally or blows up in a finite time but also compute the upper and lower bound for blow‐up time when blow‐up occurs. Additionally, two examples are given to illustrate the main results.

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“…However, their results did not include the influence of weight functions on the blow-up phenomenon. Besides, one can refer to [29][30][31] for more results about reaction-diffusion models with spacedependent coefficients.…”

Section: Introductionmentioning

confidence: 99%

Bounds for the blow-up time of a porous medium equation with weighted nonlocal source and inner absorption terms

Shen

Fang

2018

Bound Value Probl

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We investigate the blow-up phenomena for a porous medium equation with weighted nonlocal source and inner absorption terms subject to null Dirichlet boundary condition. Based on a modified differential inequality technique, we establish some sufficient conditions to guarantee the existence of non-global solutions to the model and also derive the upper bounds for the blow-up time. Moreover, the lower bounds for the blow-up time are obtained under some appropriate measure in the whole-dimensional space (N ≥ 1).

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Blow-up analysis for a reaction–diffusion equation with weighted nonlocal inner absorptions under nonlinear boundary flux

Cited by 23 publications

References 24 publications

Some Results on Blow-up Phenomenon for Nonlinear Porous Medium Equations with Weighted Source

Some Results on Blow-up Phenomenon for Nonlinear Porous Medium Equations with Weighted Source

Global and blow‐up analysis for a class of nonlinear reaction diffusion model with Dirichlet boundary conditions

Bounds for the blow-up time of a porous medium equation with weighted nonlocal source and inner absorption terms

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