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STOCHASTIC GEOMETRIC WAVE EQUATIONS WITH VALUES IN COMPACT RIEMANNIAN HOMOGENEOUS SPACES
, 2011
"... Let M be a compact Riemannian homogeneous space (e.g. a Euclidean sphere). We prove existence of a global weak solution of the stochastic wave equation ..."
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Let M be a compact Riemannian homogeneous space (e.g. a Euclidean sphere). We prove existence of a global weak solution of the stochastic wave equation
Stochastic wave equation with critical nonlinearities: temporal regularity and uniqueness
 J. Differential Equations
"... We consider a nonlinear wave equation driven by a spatially homogeneous Wiener process W with a finite spectral measure and with nonlinear terms f , g of critical growth. We study pathwise uniqueness and norm continuity of paths of (u, u t under the hypothesis that there exists a local solution u ..."
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We consider a nonlinear wave equation driven by a spatially homogeneous Wiener process W with a finite spectral measure and with nonlinear terms f , g of critical growth. We study pathwise uniqueness and norm continuity of paths of (u, u t under the hypothesis that there exists a local solution u such that (u, u t ) has weakly continuous
Inverse problem for the wave equation with a white noise source. accepted to Comm
 Math. Phys
, 2014
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SECOND ORDER PDES WITH DIRICHLET WHITE NOISE BOUNDARY CONDITIONS
, 2013
"... HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte p ..."
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HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et a ̀ la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
SECOND ORDER PDES WITH DIRICHLET WHITE NOISE BOUNDARY CONDITIONS
, 2013
"... Abstract. In this paper we study the Poisson and heat equations on bounded and unbounded domains with smooth boundary with random Dirichlet boundary conditions. The main novelty of this workis a convenient frameworkfor the analysis of such equations excited by the white in time and/or space noise on ..."
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Abstract. In this paper we study the Poisson and heat equations on bounded and unbounded domains with smooth boundary with random Dirichlet boundary conditions. The main novelty of this workis a convenient frameworkfor the analysis of such equations excited by the white in time and/or space noise on the boundary. Our approach allows us to show the existence and uniqueness of weak solutions in the space of distributions. Then we prove that the solutions can be identified as smooth functions inside the domain, and finally the rate of their blow up at the boundary is estimated. A large class of noises including Wiener and fractional Wiener space time white noise, homogeneous noise and Lévy noise is considered.
WEAK SOLUTIONS TO STOCHASTIC WAVE EQUATIONS WITH VALUES IN RIEMANNIAN MANIFOLDS
"... Abstract. Let M be a compact Riemannian manifold. We prove existence of a global weak solution of the stochastic wave equation Dt∂tu = Dx∂xu + (Xu + λ0(u)∂tu + λ1(u)∂xu) ˙ W where X is a continuous tangent vector field on M, λ0, λ1 are continuous vector bundles homomorphisms from T M to T M and W i ..."
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Abstract. Let M be a compact Riemannian manifold. We prove existence of a global weak solution of the stochastic wave equation Dt∂tu = Dx∂xu + (Xu + λ0(u)∂tu + λ1(u)∂xu) ˙ W where X is a continuous tangent vector field on M, λ0, λ1 are continuous vector bundles homomorphisms from T M to T M and W is a spatially homogeneous Wiener process on R with finite spectral measure. A new general method of constructing weak solutions of SPDEs that does not rely on martingale representation theorem is used. 1.
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"... A stochastic fractal model of the Universe related to the fractional Laplacian ..."
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A stochastic fractal model of the Universe related to the fractional Laplacian