We prove that semilinear stochastic abstract wave equations, including wave and plate equations, are well-posed in the strong sense with an α -Hölder continuous drift coefficient, if α∈(2/3,1). The uniqueness may fail for the corresponding deterministic PDE and well-posedness is restored by adding an external random forcing of white noise type. This shows a kind of regularization by noise for the semilinear wave equation. To prove the result we introduce an approach based on backward stochastic differential equations. We also establish regularizing properties of the transition semigroup associated to the stochastic wave equation by using control theoretic results

Masiero, F., Priola, E. (2017). Well-posedness of semilinear stochastic wave equations with Hölder continuous coefficients. JOURNAL OF DIFFERENTIAL EQUATIONS, 263(3), 1773-1812 [10.1016/j.jde.2017.03.031].

Well-posedness of semilinear stochastic wave equations with Hölder continuous coefficients

MASIERO, FEDERICA
Primo
;
2017

Abstract

We prove that semilinear stochastic abstract wave equations, including wave and plate equations, are well-posed in the strong sense with an α -Hölder continuous drift coefficient, if α∈(2/3,1). The uniqueness may fail for the corresponding deterministic PDE and well-posedness is restored by adding an external random forcing of white noise type. This shows a kind of regularization by noise for the semilinear wave equation. To prove the result we introduce an approach based on backward stochastic differential equations. We also establish regularizing properties of the transition semigroup associated to the stochastic wave equation by using control theoretic results
Articolo in rivista - Articolo scientifico
Nonlinear stochastic wave equation; Hölder continuous drift; Strong uniqueness
English
2017
1773
1812
40
Masiero, F., Priola, E. (2017). Well-posedness of semilinear stochastic wave equations with Hölder continuous coefficients. JOURNAL OF DIFFERENTIAL EQUATIONS, 263(3), 1773-1812 [10.1016/j.jde.2017.03.031].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/149223
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