Blow up near higher modes of nonlinear wave equations

Sternberg, Natalia

doi:10.1090/S0002-9947-1986-0837814-7

Blow up near higher modes of nonlinear wave equations

Author: Natalia Sternberg
Journal: Trans. Amer. Math. Soc. 296 (1986), 315-325
MSC: Primary 35L05; Secondary 35B35
DOI: https://doi.org/10.1090/S0002-9947-1986-0837814-7
MathSciNet review: 837814
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Abstract: This paper is concerned with the instability properties of higher modes of the nonlinear wave equation ${u_{tt}} - \Delta u - f(u) = 0$ defined on a smoothly bounded domain with Dirichlet boundary conditions. It is shown that they are unstable in the sense that in any neighborhood of a higher mode there exists a solution of the given equation which blows up in finite time.

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