An Explicit Solution of a Parabolic Equation with Nonlocal Boundary Conditions

  • A. Bastys
  • F. Ivanauskas
  • M. Sapagovas


We consider a parabolic differential equation with nonlocal boundary conditions. We find an explicit solution of the problem and prove the uniqueness of the solution. Analysis of the explicit solution reveals that it has three physically different linear components. The first component is of standing wave type, and the other two are of right- and left-going wave types, respectively. The speed of propagation of the heat waves depends on constants present in nonlocal boundary conditions. We give examples of right-going heat waves that have constant energy.


parabolic equation nonlocal boundary conditions existence of solution uniqueness explicit solution heat waves 


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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • A. Bastys
    • 1
  • F. Ivanauskas
    • 1
    • 2
  • M. Sapagovas
    • 2
  1. 1.Vilnius UniversityVilniusLithuania
  2. 2.Institute of Mathematics and InformaticsVilniusLithuania

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