Blow-up of weak solutions for the semilinear wave equations with nonlinear boundary and interior sources and damping

Volume 35 / 2008

Lorena Bociu, Irena Lasiecka Applicationes Mathematicae 35 (2008), 281-304 MSC: Primary 35L05; Secondary 35B33, 35B35, 35L20. DOI: 10.4064/am35-3-3

Abstract

We focus on the blow-up in finite time of weak solutions to the wave equation with interior and boundary nonlinear sources and dissipations. Our central interest is the relationship of the sources and damping terms to the behavior of solutions. We prove that under specific conditions relating the sources and the dissipations (namely $p > m$ and $k > m$), weak solutions blow up in finite time.

Authors

  • Lorena Bociu243 Avery Hall
    University of Nebraska-Lincoln
    Lincoln, NE 68588, U.S.A.
    e-mail
  • Irena LasieckaDepartment of Mathematics
    University of Virginia
    Charlottesville, VA 22904, U.S.A.
    e-mail

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