Global Behavior of Solutions to Chevron Pattern Equations

Abstract

Considering a system of equations modeling the chevron pattern dynamics, we show that the corresponding initial boundary value problem has a unique weak solution that continuously depends on initial data, and the semigroup generated by this problem in the phase space $X^0:=L^2(\Omega )\times L^2(\Omega )$ has a global attractor. We also provide some insight to the behavior of the system, by reducing it under special assumptions to systems of ODEs, that can in turn be studied as dynamical systems.

References in corpus (4)

• Weakly Nonlinear Theory of Pattern-Forming Systems with Spontaneously Broken Isotropy
• Pattern Formation from Defect Chaos --- A Theory of Chevrons
• Deviations from linear theory for fluctuations below the supercritical primary bifurcation to electroconvection
• Modulated structures in electroconvection in nematic liquid crystals