We introduce a class of stochastic Allen–Cahn equations with a mobility coefficient and colored noise. For initial data with finite free energy, we analyze the corresponding Cauchy problem on the d-dimensional torus in the time interval [0, T]. Assuming that d ≤ 3 and that the potential has quartic growth, we prove existence and uniqueness of the solution as a process u in L^2 with continuous paths, satisfying almost surely the regularity properties u ∈ C([0, T];H^1) and u ∈ L^2([0, T];H^2).

Stochastic Allen–Cahn equation with mobility / Bertini Malgarini, Lorenzo; Butta', Paolo; Pisante, Adriano. - In: NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS. - ISSN 1021-9722. - STAMPA. - 24:5(2017). [10.1007/s00030-017-0477-3]

Stochastic Allen–Cahn equation with mobility

BERTINI MALGARINI, Lorenzo;BUTTA', Paolo;PISANTE, Adriano
2017

Abstract

We introduce a class of stochastic Allen–Cahn equations with a mobility coefficient and colored noise. For initial data with finite free energy, we analyze the corresponding Cauchy problem on the d-dimensional torus in the time interval [0, T]. Assuming that d ≤ 3 and that the potential has quartic growth, we prove existence and uniqueness of the solution as a process u in L^2 with continuous paths, satisfying almost surely the regularity properties u ∈ C([0, T];H^1) and u ∈ L^2([0, T];H^2).
2017
stochastic PDEs; Allen–Cahn equation; Well-posedness
01 Pubblicazione su rivista::01a Articolo in rivista
Stochastic Allen–Cahn equation with mobility / Bertini Malgarini, Lorenzo; Butta', Paolo; Pisante, Adriano. - In: NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS. - ISSN 1021-9722. - STAMPA. - 24:5(2017). [10.1007/s00030-017-0477-3]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1012056
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