Skip to main content
SpringerLink
Log in

The blow-up properties of solutions to semilinear heat equations with nonlinear boundary conditions

  • Published:
Zeitschrift für angewandte Mathematik und Physik ZAMP Aims and scope Submit manuscript

Abstract.

This paper deals with the blow-up properties of solutions to semilinear heat equation \(u_t-u_{xx}=u^p \text{ in }(0,1)\times(0,T)\) with the nonlinear boundary conditions \(u_x(0,t)=0,u_x(1,t)=u^q\text{ on }[0,T)\). The necessary and sufficient conditions for the solution to have a finite time blow-up and the exact blow-up rates are established. It is also proved that the blow-up will occur only at the boundary x = 1.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Author information

Authors and Affiliations

  1. Department of Mathematics, Yangzhou University, Yangzhou 225002, China, e-mail: chzhang@yzu.edu.cn, , , , , , CN

    Z. Lin

  2. Department of Applied Mathematics, Southeast University, Nanjing 210018, China, , , , , , CN

    M. Wang

Authors
  1. Z. Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Received: November 1, 1997; revised: April 1, 1998

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lin, Z., Wang, M. The blow-up properties of solutions to semilinear heat equations with nonlinear boundary conditions. Z. angew. Math. Phys. 50, 361–374 (1999). https://doi.org/10.1007/s000330050023

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s000330050023

Search

Navigation