CONTROL DESIGN FOR A CLASS OF GENERAL NONLINEAR REACTION DIFFUSION EQUATIONS

Fushan Li; Wen Chen

doi:10.11948/20210250

2022 Volume 12 Issue 2

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Fushan Li, Wen Chen. CONTROL DESIGN FOR A CLASS OF GENERAL NONLINEAR REACTION DIFFUSION EQUATIONS[J]. Journal of Applied Analysis & Computation, 2022, 12(2): 609-621. doi: 10.11948/20210250

Citation:

Fushan Li, Wen Chen. CONTROL DESIGN FOR A CLASS OF GENERAL NONLINEAR REACTION DIFFUSION EQUATIONS[J]. Journal of Applied Analysis & Computation, 2022, 12(2): 609-621. doi: 10.11948/20210250

CONTROL DESIGN FOR A CLASS OF GENERAL NONLINEAR REACTION DIFFUSION EQUATIONS

Fushan Li^1, ,,
Wen Chen¹

1.
School of Mathematical Sciences, Qufu Normal University, Qufu, 273165, China

Corresponding author: Email: fushan99@163.com(F. Li)

Abstract

Abstract

We consider a class of nonlinear parabolic equation with general source function $f(u)$, conduction function $g(u)$ and conduction coefficient $\rho(|\nabla u|^2)$ in multi-dimensional space. We establish new control conditions to guarantee that the positive solution exists globally. At the same time, under suitable control conditions, by means of the Sobolev inequality in multi-dimensional space, we obtain upper and lower bounds of the blow-up time $t^*$ in $\mathbb{R}^{n}\, (n\geqslant 2)$. Our work generalize the models, improve the method and remove the constraint of spatial dimension in many literatures.
- Control design /
- reaction diffusion equation /
- global existence /
- blow up /
- multi-dimensional space
MSC: 35B35, 35G05, 35G16, 35L30

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References

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