Stability Properties of Space Periodic Standing Waves

  • B. Scarpellini

    Universität Basel, Switzerland

Abstract

Equilibrium solutions of parabolic systems of the form are considered, where designates as diagonal matrix, a bifurcation parameter, a state vector and a polynomial nonlinearity. A trivial solution branch , is supposed to be given, i.e. for some and every . Then a period is fixed and under suitable assumptions space--periodic bifurcating standing waves are constructed. It is shown that these bifurcating branches become generically unstable as . Under the condition of however, they will remain stable against -periodic perturbations , provided that the trivial solution-branch behaves alike for small . The so-called Landau-Ginzburg equations arising in Landau’s theory of phase transitions constitute a special example in physics.

Cite this article

B. Scarpellini, Stability Properties of Space Periodic Standing Waves. Z. Anal. Anwend. 6 (1987), no. 6, pp. 485–503

DOI 10.4171/ZAA/267