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On some numerical aspects for some fractional stochastic partial differential equations / Arab,Zineb
Titre : On some numerical aspects for some fractional stochastic partial differential equations : Case of Burgers equation Type de document : texte imprimé Auteurs : Arab,Zineb, Auteur ; Debbi,Latifa, Directeur de thèse Editeur : Setif:UFA Année de publication : 2021 Importance : 1 vol (153 f .) Format : 29 cm Langues : Français (fre) Catégories : Thèses & Mémoires:Mathématique Mots-clés : Fractional stochastic Burgers-type equation
Fractional stochastic nonlinear heat equation
Fractional LaplacianIndex. décimale : 510 Mathématique Résumé :
This dissertation has provided a rigorous analysis of various numerical
schemes for a class of local and global Lipschitz nonlinear fractional stochastic
partial differential equations, driven by the fractional Laplacian in the
one dimensional space and perturbed by a Gaussian noise. The study
contains the elaboration of time, space and space-time schemes and their
different convergences. Specially, we express for every scheme the rate of
convergence in terms of the fractional power of the Laplacian.
The first contribution (Chapter 5) concerned the study of the fractional
stochastic Burgers-type equation in Hölder space C(0, 1), with diffusion
dissipation index 2 (74
, 2]. We have proved the existence and the uniqueness
of a space-time Hölder mild solution. Moreover, we have fulfilled the
pathwise convergence of the spacial and the full approximations, where
the spectral Galerkin method has been used for the spacial approximation,
whereas the exponential Euler scheme has been used for the temporal approximation.
In the second contribution (Chapter 6), we have considered the fractional
stochastic nonlinear heat equation in the Hilbert space L2(0, 1),
with diffusion dissipation index 2 (1, 2]. By using the spectral Galerkin
method for the spacial approximation and the implicit Euler scheme for
the temporal approximation, we have established the strong convergence
in the space Lp(
, L2(0, 1)) of the temporal, the spacial and the full ap-
1
proximations of the mild solution.
In the third contribution (Chapter 7), we have improved the diffusion
dissipation index obtained in Chapter 5 to 2 (3
2, 2], by proving a weaker
convergence (i.e. convergence in probability) of the temporal approxiL
of the fractional stochastic Burgers equation in the Hilbert space L2(0, 1).Côte titre : DM/0163 En ligne : http://dspace.univ-setif.dz:8888/jspui/bitstream/123456789/3779/1/these.pdf Format de la ressource électronique : On some numerical aspects for some fractional stochastic partial differential equations : Case of Burgers equation [texte imprimé] / Arab,Zineb, Auteur ; Debbi,Latifa, Directeur de thèse . - [S.l.] : Setif:UFA, 2021 . - 1 vol (153 f .) ; 29 cm.
Langues : Français (fre)
Catégories : Thèses & Mémoires:Mathématique Mots-clés : Fractional stochastic Burgers-type equation
Fractional stochastic nonlinear heat equation
Fractional LaplacianIndex. décimale : 510 Mathématique Résumé :
This dissertation has provided a rigorous analysis of various numerical
schemes for a class of local and global Lipschitz nonlinear fractional stochastic
partial differential equations, driven by the fractional Laplacian in the
one dimensional space and perturbed by a Gaussian noise. The study
contains the elaboration of time, space and space-time schemes and their
different convergences. Specially, we express for every scheme the rate of
convergence in terms of the fractional power of the Laplacian.
The first contribution (Chapter 5) concerned the study of the fractional
stochastic Burgers-type equation in Hölder space C(0, 1), with diffusion
dissipation index 2 (74
, 2]. We have proved the existence and the uniqueness
of a space-time Hölder mild solution. Moreover, we have fulfilled the
pathwise convergence of the spacial and the full approximations, where
the spectral Galerkin method has been used for the spacial approximation,
whereas the exponential Euler scheme has been used for the temporal approximation.
In the second contribution (Chapter 6), we have considered the fractional
stochastic nonlinear heat equation in the Hilbert space L2(0, 1),
with diffusion dissipation index 2 (1, 2]. By using the spectral Galerkin
method for the spacial approximation and the implicit Euler scheme for
the temporal approximation, we have established the strong convergence
in the space Lp(
, L2(0, 1)) of the temporal, the spacial and the full ap-
1
proximations of the mild solution.
In the third contribution (Chapter 7), we have improved the diffusion
dissipation index obtained in Chapter 5 to 2 (3
2, 2], by proving a weaker
convergence (i.e. convergence in probability) of the temporal approxiL
of the fractional stochastic Burgers equation in the Hilbert space L2(0, 1).Côte titre : DM/0163 En ligne : http://dspace.univ-setif.dz:8888/jspui/bitstream/123456789/3779/1/these.pdf Format de la ressource électronique : Exemplaires (1)
Code-barres Cote Support Localisation Section Disponibilité DM/0163 DM/0163 Thèse Bibliothéque des sciences Anglais Disponible
Disponible