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International Symposium on Neural Networks

ISNN 2011: Advances in Neural Networks – ISNN 2011 pp 222–230Cite as

Blow-Up for a Class of Parabolic Equations with Nonlinear Boundary Conditions

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6675))

Abstract

In this paper, we consider the following equation

\(\frac{\partial h(u)}{\partial t}=\Delta u+a(x,t)f(u),\quad \Omega\times(0,T),\)

with initial condition and third boundary condition. By constructing an auxiliary function and using maximum principles, we established a sufficient conditions for the blow-up of solutions. The blow-up rate and the blow-up set were also considered under appropriate assumption. This result generalizes and improves earlier results in literatures.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Chongqing Jiaotong University, Chongqing, 400074, China

    Leina Zhao

Authors
  1. Leina Zhao
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Editor information

Editors and Affiliations

  1. Institute of Automation, Key Laboratory of Complex Systems and Intelligence Science, Chinese Academy of Sciences, 100190, Beijing, China

    Derong Liu

  2. College of Information Science and Engineering, Shenyang, Northeastern University, 110004, Liaoing, China

    Huaguang Zhang

  3. Department of Electrical and Computer Engineering, University of Cyprus, 75 Kallipoleos Avenue, 1678, Nicosia, Cyprus

    Marios Polycarpou

  4. Dipartimento di Elettronica, Politecnico di Milano, Piazza L. da Vinci 32, 20133, Milano, Italy

    Cesare Alippi

  5. Deptartment of Electrical, Computer and Biomedical Engineering, University of Rhode Island, RI 02881, Kingston, USA

    Haibo He

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© 2011 Springer-Verlag Berlin Heidelberg

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Zhao, L. (2011). Blow-Up for a Class of Parabolic Equations with Nonlinear Boundary Conditions. In: Liu, D., Zhang, H., Polycarpou, M., Alippi, C., He, H. (eds) Advances in Neural Networks – ISNN 2011. ISNN 2011. Lecture Notes in Computer Science, vol 6675. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21105-8_27

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  • DOI: https://doi.org/10.1007/978-3-642-21105-8_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21104-1

  • Online ISBN: 978-3-642-21105-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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