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Stochastic Phase Field Equations: Existence and Uniqueness

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Abstract.

We consider a conservative system of stochastic PDE's, namely a one dimensional phase field model perturbed by an additive space-time white noise. We prove a global existence and uniqueness result in a space of continuous functions on \( \mathbb{R}_{+} \times \mathbb{R} \). This result is obtained by extending previous results of Doering [3] on the stochastic Allen-Cahn equation.

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Submitted 30/01/01, accepted 13/06/01

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Bertini, L., Brassesco, S., Buttà, P. et al. Stochastic Phase Field Equations: Existence and Uniqueness. Ann. Henri Poincaré 3, 87–98 (2002). https://doi.org/10.1007/s00023-002-8612-y

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Keywords

  • Continuous Function
  • White Noise
  • Field Equation
  • Field Model
  • Global Existence