A+ CATEGORY SCIENTIFIC UNIT

The principal spectrum for linear nonautonomous parabolic PDEs of second order: Space-independent case

Volume 90 / 2001

Janusz Mierczy/nski Colloquium Mathematicum 90 (2001), 95-100 MSC: 35K99, 35P15. DOI: 10.4064/cm90-1-8

Abstract

We show that the study of the principal spectrum of a linear nonautonomous parabolic PDE of second order $u_t={{\mit \Delta }}u+a(t)u$ on a bounded domain, with the Dirichlet or Neumann boundary conditions, reduces to the investigation of the spectrum of the linear nonautonomous ODE $\dot {v}=a(t)v$.

Authors

  • Janusz Mierczy/nskiInstitute of Mathematics
    Wroc/law University of Technology
    Wybrze/ze Wyspiańskiego 27
    50-370 Wroc/law, Poland
    e-mail

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