Solvability of coupled FBSDEs with diagonally quadratic generators

2017 ◽  
Vol 17 (06) ◽  
pp. 1750043 ◽  
Author(s):  
Peng Luo ◽  
Ludovic Tangpi
Keyword(s):  
Existence And Uniqueness ◽  
Small Time ◽  
Coupled Systems ◽  
Time Interval ◽  
Well Posedness ◽  
Initial Value ◽  
Small Time Interval ◽  
Uniqueness Of The Solution ◽  
Backward Sdes

We study the well-posedness for multi-dimensional and coupled systems of forward–backward SDEs when the generator can be separated into a quadratic and a subquadratic part. We obtain the existence and uniqueness of the solution on a small time interval. Moreover, the continuity and differentiability with respect to the initial value are presented.

scholarly journals INVERSE PROBLEM FOR THE TIME-FRACTIONAL EULER-BERNOULLI BEAM EQUATION

2021 ◽  
Vol 26 (3) ◽  
pp. 503-518
Author(s):  
Ibrahim Tekin ◽  
He Yang
Keyword(s):  
Existence And Uniqueness ◽  
Numerical Experiments ◽  
Small Time ◽  
Beam Equation ◽  
Time Interval ◽  
Existence And Uniqueness Theorem ◽  
Bernoulli Beam ◽  
Additional Measurement ◽  
Small Time Interval ◽  
Euler Bernoulli Beam

In this paper, the classical Euler-Bernoulli beam equation is considered by utilizing fractional calculus. Such an equation is called the time-fractional EulerBernoulli beam equation. The problem of determining the time-dependent coefficient for the fractional Euler-Bernoulli beam equation with homogeneous boundary conditions and an additional measurement is considered, and the existence and uniqueness theorem of the solution is proved by means of the contraction principle on a sufficiently small time interval. Numerical experiments are also provided to verify the theoretical findings.

scholarly journals On the Solvability of the Identification Problem for a Source Function in a Quasilinear Parabolic System of Equations in Bounded and Unbounded Domains

2001 ◽  
Vol 14 (4) ◽  
pp. 483-491
Author(s):  
Vera G. Kopylova ◽  
Keyword(s):  
Source Function ◽  
Splitting Method ◽  
Identification Problem ◽  
Cauchy Data ◽  
Rectangular Domain ◽  
Small Time ◽  
Time Interval ◽  
Weak Approximation ◽  
Small Time Interval ◽  
Uniqueness Of The Solution

The paper considers the problem of identification for a source function in one of two equations of parabolic quasilinear system. The case of Cauchy data in an unbounded domain and the case of boundary conditions of the first kind in a rectangular domain are considered. The question of the existence and uniqueness of the solution is studied. The proof uses a differential level splitting method known as the weak approximation method. The solution is obtained on a small time interval in the class of sufficiently smooth bounded functions

On diffracted wave fronts

1979 ◽  
Vol 84 (1-2) ◽  
pp. 35-54
Author(s):  
Peter Wolfe
Keyword(s):  
Wave Equation ◽  
Wave Front ◽  
Incident Wave ◽  
Spherical Wave ◽  
Small Time ◽  
Time Interval ◽  
Wave Fronts ◽  
Incident Plane ◽  
Small Time Interval ◽  
Propagation Of Singularities

SynopsisIn this paper we study the wave equation, in particular the propagation of discontinuities. Two problems are considered: diffraction of a normally incident plane pulse by a plane screen and diffraction of a spherical wave by the same screen. It is shown that when an incident wave front strikes the edge of the screen a diffracted wave front is produced. The discontinuities are precisely computed in a neighbourhood of the edge for a small time interval after the arrival of the incident wave front and a theorem of Hörmander on the propagation of singularities is used to obtain a globalresult.

GENERIC QUANTUM MARKOV SEMIGROUPS, CYCLE DECOMPOSITION AND DEVIATION FROM EQUILIBRIUM

2012 ◽  
Vol 15 (03) ◽  
pp. 1250016 ◽  
Author(s):  
FRANCO FAGNOLA ◽  
VERONICA UMANITÀ
Keyword(s):  
Small Time ◽  
Jump Processes ◽  
Time Interval ◽  
Markov Semigroup ◽  
Cycle Decomposition ◽  
Markov Jump ◽  
Partial Isometries ◽  
Small Time Interval ◽  
Positive Weights ◽  
The Difference

A generic quantum Markov semigroup [Formula: see text] of a d-level quantum open system with a faithful normal invariant state ρ admits a dual semigroup [Formula: see text] with respect to the scalar product induced by ρ. We show that the difference of the generators [Formula: see text] can be written as the sum of a derivation 2i[H, ⋅] and a weighted difference of automorphisms [Formula: see text] where [Formula: see text] is a family of cycles on the d levels of the system, wc are positive weights and [Formula: see text] are unitaries. This formula allows us to represent the deviation from equilibrium (in a "small" time interval) as the superposition of cycles of the system where the difference between the forward and backward evolution is written as the difference of a reversible evolution and its time reversal. Moreover, it generalises cycle decomposition of Markov jump processes. We also find a similar formula with partial isometries instead of unitaries.

scholarly journals Discrete Mittag-Leffler Functions in Linear Fractional Difference Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-21 ◽  
Author(s):  
Jan Čermák ◽  
Tomáš Kisela ◽  
Luděk Nechvátal
Keyword(s):  
Existence And Uniqueness ◽  
Initial Conditions ◽  
Linear Difference Equation ◽  
Discrete Fractional Calculus ◽  
Initial Value ◽  
Fractional Difference ◽  
Uniqueness Of The Solution ◽  
Discrete Analogues ◽  
Fractional Type ◽  
Special Time

This paper investigates some initial value problems in discrete fractional calculus. We introduce a linear difference equation of fractional order along with suitable initial conditions of fractional type and prove the existence and uniqueness of the solution. Then the structure of the solutions space is discussed, and, in a particular case, an explicit form of the general solution involving discrete analogues of Mittag-Leffler functions is presented. All our observations are performed on a special time scale which unifies and generalizes ordinary difference calculus andq-difference calculus. Some of our results are new also in these particular discrete settings.

Gaussian approximation of some closed stochastic epidemic models

1977 ◽  
Vol 14 (02) ◽  
pp. 221-231
Author(s):  
Frank J. S. Wang
Keyword(s):  
Epidemic Model ◽  
Limit Theorems ◽  
Gaussian Approximation ◽  
Infected Individual ◽  
Small Time ◽  
Entire Population ◽  
Time Interval ◽  
Stochastic Epidemic Models ◽  
Small Time Interval ◽  
Stochastic Epidemic

A generalization of Bailey's general epidemic model is considered. In this generalized model, it is assumed that the probability of any particular susceptible becoming infected during the small time interval (t, t + Δt) is α(X(t))Δt + o(Δt), for some function a, where X(t) is the proportion of infected individuals in the entire population, the probability that an infected individual is infected for at least a length of time t is F(t), and recovered individuals are permanently immune from further attack. In this paper, central limit theorems are obtained for the proportion of infected individuals and the proportion of susceptibles in the entire population.

scholarly journals A LARGE DEFORMATION, VISCOELASTIC, THIN ROD MODEL: DERIVATION AND ANALYSIS

2009 ◽  
Vol 19 (10) ◽  
pp. 1907-1928 ◽  
Author(s):  
J. BEYROUTHY ◽  
H. LE DRET
Keyword(s):  
Existence And Uniqueness ◽  
Finite Strain ◽  
Three Dimensional ◽  
Evolution Problem ◽  
Well Posedness ◽  
One Dimensional ◽  
Uniqueness Of The Solution ◽  
Model Derivation ◽  
Regularity Results ◽  
Strain Model

We present a Cosserat-based three-dimensional to one-dimensional reduction in the case of a thin rod, of the viscoelastic finite strain model introduced by Neff. This model is a coupled minimization/evolution problem. We prove the existence and uniqueness of the solution of the reduced minimization problem. We also show a few regularity results for this solution which allow us to establish the well-posedness of the evolution problem. Finally, the reduced model preserves observer invariance.

A nonlinear pseudoparabolic equation

1990 ◽  
Vol 114 (1-2) ◽  
pp. 119-133 ◽  
Author(s):  
Dang Dinh Ang ◽  
Tran Thanh
Keyword(s):  
Salient Feature ◽  
Small Time ◽  
Time Interval ◽  
Pseudoparabolic Equation ◽  
Nonhomogeneous Boundary ◽  
Small Time Interval ◽  
Nonhomogeneous Boundary Conditions ◽  
Image Position ◽  
Special Case ◽  
Nonlinear Pseudoparabolic Equation

SynopsisThe authors prove results on uniqueness and global existence of initial and boundary value problems for the nonlinear pseudoparabolic equationwith nonhomogeneous boundary conditions. A salient feature of the paper is that F and its partial derivatives are allowed to be unbounded. In the special case b(x, t)= α2 (a positive constant), it is proved that the corresponding solution uα, under appropriate conditions on the data (which are satisfied, for example, by the Benjamin–Bona–Mahony equation), uα→ u0 the solution corresponding to β = 0, on sufficiently small time interval. A result on the asymptotic behaviour of the solution is given for t → ∞.

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