Numerical Continuation and SPDE Stability for the 2D Cubic-Quintic Allen-Cahn Equation

  title={Numerical Continuation and SPDE Stability for the 2D Cubic-Quintic Allen-Cahn Equation},
  author={C. K{\"u}hn},
  journal={SIAM/ASA J. Uncertain. Quantification},
  • C. Kühn
  • Published 2015
  • Mathematics, Physics, Computer Science
  • SIAM/ASA J. Uncertain. Quantification
  • We study the Allen--Cahn equation with a cubic-quintic nonlinear term and a $Q$-trace-class stochastic forcing in two spatial dimensions. This stochastic partial differential equation (SPDE) is used as a test case to understand how numerical continuation methods can be carried over to the SPDE setting. First, we compute the deterministic bifurcation diagram for the PDE, i.e., without stochastic forcing. In this case, two locally asymptotically stable steady state solution branches exist upon… CONTINUE READING
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