scholarly journals Existence and uniqueness of solutions for two- dimensional fractional non- colliding particle systems

2020 ◽  
Vol 71 (1) ◽  
pp. 11-17
Author(s):  
Huong Vu Thi
Keyword(s):  
Diffusion Coefficients ◽  
Existence And Uniqueness ◽  
Particle Systems ◽  
Electrostatic Repulsion ◽  
Nearest Neighbour ◽  
Two Dimensional ◽  
Stochastic Evolution ◽  
Uniqueness Of Solutions ◽  
Restoring Force ◽  
Brownian Particles

In this paper, we consider the stochastic evolution of two particles with electrostatic repulsion and restoring force which is modeled by a system of stochastic differential equations driven by fractional Brownian motion where the diffusion coefficients are constant. This is the simplest case for some classes of non- colliding particle systems such as Dyson Brownian motions, Brownian particles systems with nearest neighbour repulsion. We will prove that the equation has a unique non- colliding solution in path- wise sense.

scholarly journals Existence and Uniqueness of Solutions for Delay Stochastic Evolution Equations of Second Order in Time

2003 ◽  
Vol 03 (02) ◽  
pp. 141-167 ◽  
Author(s):  
María J. Garrido-Atienza ◽  
José Real
Keyword(s):  
Existence And Uniqueness ◽  
Evolution Equations ◽  
Second Order ◽  
Point Of View ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Uniqueness Of Solutions ◽  
Second Order In Time ◽  
Functional Setting

Some results on the existence and uniqueness of solutions for stochastic evolution equations of second order in time, containing some hereditary characteristics, are proved. Our theory is developed from a variational point of view and in a general functional setting which permit us to deal with several kinds of delay terms in a unified formulation. The theory is illustrated with two examples.

scholarly journals On a two-dimensional fractional thermoelastic system with nonlocal constraints describing a fractional Kirchhoff plate

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Said Mesloub ◽  
Faten Aldosari
Keyword(s):  
Existence And Uniqueness ◽  
Energy Inequality ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Kirchhoff Plate ◽  
Two Dimensional ◽  
Uniqueness Of Solutions ◽  
Fractional Caputo Derivative ◽  
Kirchhoff Plate Model ◽  
Nonlocal Constraints

AbstractWe show herein the existence and uniqueness of solutions for coupled fractional order partial differential equations modeling a thermoelastic fractional Kirchhoff plate model associated with initial, Dirichlet, and nonlocal boundary conditions involving fractional Caputo derivative. Some efficient results of existence and uniqueness are obtained by employing the energy inequality method.

scholarly journals ON STOCHASTIC EVOLUTION EQUATIONS WITH NON-LIPSCHITZ COEFFICIENTS

2009 ◽  
Vol 09 (04) ◽  
pp. 549-595 ◽  
Author(s):  
XICHENG ZHANG
Keyword(s):  
Existence And Uniqueness ◽  
Evolution Equations ◽  
Reaction Diffusion ◽  
Stochastic Equations ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Uniqueness Of Solutions ◽  
Volterra Type ◽  
Porous Medium Equations ◽  
Stochastic Functional

In this paper, we study the existence and uniqueness of solutions for several classes of stochastic evolution equations with non-Lipschitz coefficients, that contains backward stochastic evolution equations, stochastic Volterra type evolution equations and stochastic functional evolution equations. In particular, the results can be used to treat a large class of quasi-linear stochastic equations, which includes the reaction diffusion and porous medium equations.

scholarly journals On the well-posedness of the anisotropically-reduced two-dimensional Kuramoto-Sivashinsky Equation

2022 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
David Massatt
Keyword(s):  
Initial Data ◽  
Global Existence ◽  
Existence And Uniqueness ◽  
Well Posedness ◽  
Two Dimensional ◽  
Periodic Domain ◽  
Uniqueness Of Solutions ◽  
Global Existence And Uniqueness ◽  
Sivashinsky Equation

<p style='text-indent:20px;'>We address the global existence and uniqueness of solutions for the anisotropically reduced 2D Kuramoto-Sivashinsky equations in a periodic domain with initial data <inline-formula><tex-math id="M1">\begin{document}$ u_{01} \in L^2 $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M2">\begin{document}$ u_{02} \in H^{-1 + \eta} $\end{document}</tex-math></inline-formula> for <inline-formula><tex-math id="M3">\begin{document}$ \eta &gt; 0 $\end{document}</tex-math></inline-formula>.</p>

scholarly journals Existence and Uniqueness of Solutions for a Class of Nonlinear Stochastic Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Iryna Volodymyrivna Komashynska
Keyword(s):  
Differential Equations ◽  
Diffusion Process ◽  
Stochastic Differential Equations ◽  
Successive Approximation ◽  
Diffusion Coefficients ◽  
Existence And Uniqueness ◽  
Uniqueness Result ◽  
Uniqueness Of Solutions ◽  
Nonlinear Stochastic Differential Equations

By using successive approximation, we prove existence and uniqueness result for a class of nonlinear stochastic differential equations. Moreover, it is shown that the solution of such equations is a diffusion process and its diffusion coefficients are found.

WIENER–POISSON TYPE MULTIVALUED STOCHASTIC EVOLUTION EQUATIONS IN BANACH SPACES

2012 ◽  
Vol 12 (02) ◽  
pp. 1150015 ◽  
Author(s):  
JING WU
Keyword(s):  
Differential Equations ◽  
Existence And Uniqueness ◽  
Evolution Equations ◽  
Markov Property ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Uniqueness Of Solutions ◽  
Abstract Spaces ◽  
Stochastic Ordinary Differential Equations ◽  
Poisson Type

We prove the existence and uniqueness of solutions to Wiener–Poisson type multivalued stochastic evolution equations in abstract spaces. We also prove that the solution has the Markov property. Moreover, applications to stochastic ordinary differential equations and stochastic partial differential equations are presented.

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