Existence and uniqueness of solutions to a class of stochastic partial differential equations

1985 ◽  
Vol 3 (3) ◽  
pp. 315-339 ◽  
Author(s):  
Piermarco Cannarsa ◽  
Vincenzo Vespri
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Partial Differential Equations ◽  
Existence And Uniqueness ◽  
Uniqueness Of Solutions ◽  
Partial Differential

Reflected stochastic partial differential equations with jumps

2021 ◽  
pp. 2250002
Author(s):  
Hongchao Qian ◽  
Jun Peng
Keyword(s):  
Brownian Motion ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Partial Differential Equations ◽  
Existence And Uniqueness ◽  
Random Measure ◽  
Poisson Random Measure ◽  
Uniqueness Of Solutions ◽  
Partial Differential ◽  
Penalization Method

In this paper, we establish the existence and uniqueness of solutions of reflected stochastic partial differential equations (SPDEs) driven both by Brownian motion and by Poisson random measure in a convex domain. Penalization method plays a crucial role.

DISSIPATIVE BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS IN INFINITE DIMENSIONS

2006 ◽  
Vol 09 (01) ◽  
pp. 155-168 ◽  
Author(s):  
FULVIA CONFORTOLA
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Hilbert Spaces ◽  
Stochastic Partial Differential Equations ◽  
Existence And Uniqueness ◽  
Backward Stochastic Differential Equations ◽  
Uniqueness Result ◽  
Infinite Dimensions ◽  
Partial Differential

We prove an existence and uniqueness result for a class of backward stochastic differential equations (BSDE) with dissipative drift in Hilbert spaces. We also give examples of stochastic partial differential equations which can be solved with our result.

scholarly journals Comparison theorems for multicomponent diffusion systems: developments since 1961

2000 ◽  
Vol 4 (2) ◽  
pp. 151-163
Author(s):  
M. I. Nelson
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Existence And Uniqueness ◽  
Multicomponent Diffusion ◽  
Comparison Theorems ◽  
Numerical Techniques ◽  
Uniqueness Of Solutions ◽  
Partial Differential ◽  
Diffusion Systems ◽  
Component Systems

Comparison theorems may be used to prove the existence and uniqueness of solutions to certain types of partial differential equations. They provide bounds for solutions and can be used as the basis of numerical techniques for the computation of solutions. In 1961 Alex McNabb published one of the first papers extending their use to multi-component systems. Developments in the theory and applications of such results, through citations of this original paper, are reviewed.

scholarly journals Mean-Field Forward-Backward Doubly Stochastic Differential Equations and Related Nonlocal Stochastic Partial Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Qingfeng Zhu ◽  
Yufeng Shi
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Stochastic Partial Differential Equations ◽  
Existence And Uniqueness ◽  
Mean Field ◽  
Partial Differential ◽  
Existence And Uniqueness Results ◽  
Doubly Stochastic ◽  
Uniqueness Results

Mean-field forward-backward doubly stochastic differential equations (MF-FBDSDEs) are studied, which extend many important equations well studied before. Under some suitable monotonicity assumptions, the existence and uniqueness results for measurable solutions are established by means of a method of continuation. Furthermore, the probabilistic interpretation for the solutions to a class of nonlocal stochastic partial differential equations (SPDEs) combined with algebra equations is given.

scholarly journals Stationary in Distributions of Numerical Solutions for Stochastic Partial Differential Equations with Markovian Switching

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Yi Shen ◽  
Yan Li
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Partial Differential Equations ◽  
Existence And Uniqueness ◽  
Numerical Solutions ◽  
Mild Solutions ◽  
Sufficient Conditions ◽  
Markovian Switching ◽  
Partial Differential ◽  
Stationary Distributions

We investigate a class of stochastic partial differential equations with Markovian switching. By using the Euler-Maruyama scheme both in time and in space of mild solutions, we derive sufficient conditions for the existence and uniqueness of the stationary distributions of numerical solutions. Finally, one example is given to illustrate the theory.

scholarly journals On a system of nonlinear partial differential equations

2005 ◽  
Vol 71 (3) ◽  
pp. 435-446
Author(s):  
A. Sanih Bonfoh
Keyword(s):  
Free Energy ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Existence And Uniqueness ◽  
Nonlinear Partial Differential Equations ◽  
Uniqueness Of Solutions ◽  
Partial Differential

We consider a generalised Cahn-Hilliard system with elasticity based on constitutives laws proposed by Gurtin, with a logarithmic free energy. We obtain some results on the existence and uniqueness of solutions.

Hyperbolic Stochastic Partial Differential Equations with Additive Fractional Brownian Sheet

2003 ◽  
Vol 03 (02) ◽  
pp. 121-139 ◽  
Author(s):  
Mohamed Erraoui ◽  
Youssef Ouknine ◽  
David Nualart
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Strong Solution ◽  
Stochastic Partial Differential Equations ◽  
Existence And Uniqueness ◽  
Approximation Scheme ◽  
Borel Function ◽  
Brownian Sheet ◽  
Fractional Brownian Sheet ◽  
Partial Differential

Let [Formula: see text] be a fractional Brownian sheet with Hurst parameters H, H′ ≤ 1/2. We prove the existence and uniqueness of a strong solution for a class of hyperbolic stochastic partial differential equations with additive fractional Brownian sheet of the form [Formula: see text], where b(ζ, x) is a Borel function satisfying some growth and monotonicity assumptions. We also prove the convergence of Euler's approximation scheme for this equation.

scholarly journals Singular integro-differential equations with applications

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Mohammed Al Horani ◽  
Angelo Favini ◽  
Hiroki Tanabe
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Existence And Uniqueness ◽  
Uniqueness Of Solutions ◽  
Partial Differential ◽  
Differential Problem

<p style='text-indent:20px;'>We are devoted with singular integro-differential abstract Cauchyproblems. Required conditions on spaces and operators are givenguaranteeing existence and uniqueness of solutions. Applications from partial differential equations are given to illustrate the abstract singular integro-differential problem.</p>

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