Blow-Up Phenomena for Nonlinear Reaction-Diffusion Equations under Nonlinear Boundary Conditions
Author
Source
Issue
Vol. 2016, Issue 2016 (31 Dec. 2016), pp.1-7, 7 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2016-03-20
Country of Publication
Egypt
No. of Pages
7
Main Subjects
Abstract EN
This paper deals with blow-up and global solutions of the following nonlinear reaction-diffusion equations under nonlinear boundary conditions: g(u)t=∇·au∇u+fu in Ω×0,T, ∂u/∂n=bx,u,t on ∂Ω×(0,T), u(x,0)=u0(x)>0, in Ω¯, where Ω⊂RN (N≥2) is a bounded domain with smooth boundary ∂Ω.
We obtain the conditions under which the solutions either exist globally or blow up in a finite time by constructing auxiliary functions and using maximum principles.
Moreover, the upper estimates of the “blow-up time,” the “blow-up rate,” and the global solutions are also given.
American Psychological Association (APA)
Ding, Juntang. 2016. Blow-Up Phenomena for Nonlinear Reaction-Diffusion Equations under Nonlinear Boundary Conditions. Journal of Function Spaces،Vol. 2016, no. 2016, pp.1-7.
https://search.emarefa.net/detail/BIM-1108651
Modern Language Association (MLA)
Ding, Juntang. Blow-Up Phenomena for Nonlinear Reaction-Diffusion Equations under Nonlinear Boundary Conditions. Journal of Function Spaces No. 2016 (2016), pp.1-7.
https://search.emarefa.net/detail/BIM-1108651
American Medical Association (AMA)
Ding, Juntang. Blow-Up Phenomena for Nonlinear Reaction-Diffusion Equations under Nonlinear Boundary Conditions. Journal of Function Spaces. 2016. Vol. 2016, no. 2016, pp.1-7.
https://search.emarefa.net/detail/BIM-1108651
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1108651