Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/de-gruyter/splitting-up-scheme-for-nonlinear-stochastic-hyperbolic-equations-n73rtsVXWo
References (27)
-
J. Kim (2008)
On a stochastic wave equation with unilateral boundary conditionsTransactions of the American Mathematical Society, 360
-
Z. Brzeźniak, B. Maslowski, Jan Seidler (2005)
Stochastic nonlinear beam equationsProbability Theory and Related Fields, 132
-
R. Phillips (1957)
Dissipative hyperbolic systemsTransactions of the American Mathematical Society, 86
-
A. Bensoussan, Roman Glowinski, A. Rășcanu (1992)
Approximation of some stochastic differential equations by the splitting up methodApplied Mathematics and Optimization, 25
-
M. Sango (2010)
Magnetohydrodynamic turbulent flows: Existence resultsPhysica D: Nonlinear Phenomena, 239
-
M. Sango (2007)
Weak solutions for a doubly degenerate quasilinear parabolic equation with random forcingDiscrete and Continuous Dynamical Systems-series B, 7
-
V. Barbu, G. Prato (2002)
The Stochastic Nonlinear Damped Wave EquationApplied Mathematics & Optimization, 46
-
T. Hagstrom, J. Lorenz (1998)
ALL-TIME EXISTENCE OF CLASSICAL SOLUTIONS FOR SLIGHTLY COMPRESSIBLE FLOWSSiam Journal on Mathematical Analysis, 29
-
Alain Bensoussan (1995)
Stochastic Navier-Stokes EquationsActa Applicandae Mathematica, 38
-
N. Goncharuk, P. Kotelenez (1998)
Fractional step method for stochastic evolution equationsStochastic Processes and their Applications, 73
-
R. Temam (1968)
Sur la stabilité et la convergence de la méthode des pas fractionnairesAnnali di Matematica Pura ed Applicata, 79
-
V. Anh, W. Grecksch, A. Wadewitz (1999)
A splitting method for stochastic goursat problemStochastic Analysis and Applications, 17
-
M. Sango (2010)
DENSITY DEPENDENT STOCHASTIC NAVIER–STOKES EQUATIONS WITH NON-LIPSCHITZ RANDOM FORCINGReviews in Mathematical Physics, 22
-
S. Peszat (2002)
The Cauchy problem for a nonlinear stochastic wave equation in any dimensionJournal of Evolution Equations, 2
-
J. Simon (1986)
Compact sets in the spaceLp(O,T; B)Annali di Matematica Pura ed Applicata, 146
-
P. Chow (2006)
Asymptotics of solutions to semilinear stochastic wave equationsarXiv: Probability
-
V. Barbu, G. Prato, L. Tubaro (2007)
Stochastic wave equations with dissipative dampingStochastic Processes and their Applications, 117
-
D. Gatarek, B. Goldys (1994)
On weak solutions of stochastic equations in Hilbert spacesStochastics and Stochastics Reports, 46
-
M. Sango (2005)
Existence result for a doubly degenerate quasilinear stochastic parabolic equation, 81
-
J. Lions, W. Strauss (1965)
Some non-linear evolution equationsBulletin de la Société Mathématique de France, 93
-
R. Temam (1969)
Sur l'approximation de la solution des équations de Navier-Stokes par la méthode des pas fractionnaires (II)Archive for Rational Mechanics and Analysis, 33
-
P. Chow (2002)
Stochastic Wave Equations with Polynomial NonlinearityAnnals of Applied Probability, 12
-
N. Nagase (1995)
Remarks on Nonlinear Stochastic Partial Differential Equations: An Application of the Splitting-Up MethodSiam Journal on Control and Optimization, 33
-
P. Razafimandimby, M. Sango (2010)
Asymptotic behavior of solutions of stochastic evolution equations for second grade fluidsComptes Rendus Mathematique, 348
-
I. Gyöngy, N. Krylov (2003)
On the splitting-up method and stochastic partial differential equationsAnnals of Probability, 31
-
S. Peszat, J. Zabczyk (2000)
Nonlinear stochastic wave and heat equationsProbability Theory and Related Fields, 116
-
T. Funaki (1983)
Random motion of strings and related stochastic evolution equationsNagoya Mathematical Journal, 89
- Publisher
- de Gruyter
- Copyright
- Copyright © 2013 by the
- ISSN
- 0933-7741
- eISSN
- 1435-5337
- DOI
- 10.1515/form.2011.138
- Publisher site
- See Article on Publisher Site
Abstract
Abstract. In the present paper we develop the splitting-up scheme (so-called method of fractional steps) for the investigation of existence problem for a class of nonlinear hyperbolic equations containing some nonlinear terms which do not satisfy the Lipschitz condition. Through a careful blending of the numerical scheme and deep compactness results of both analytic and probabilistic nature we establish the existence of a weak probabilistic solution for the problem. Our work is the stochastic counterpart of some important results of Roger Temam obtained in the late sixties of the last century in his works on the development of the splitting-up method for deterministic evolution problems.
Journal
Forum Mathematicum – de Gruyter
Published: Sep 1, 2013