Local Inference by Penalization Method for Biclustering Model

In this paper, we study the existence and concentration behaviour of multi-peak standing waves for a singularly perturbed Davey–Stewartson system, which arises in the theory of shallow water waves. For this purpose, we first give a sharp threshold of the existence of ground-state solutions to the related limiting problem. Next, combining the penalization method and the regularity theory of elliptic equations, we construct a family of positive solutions concentrating around any prescribed finite set of local minima, possibly degenerate, of the potential. A feature of this analysis is that we do not need any uniqueness or non-degeneracy conditions for the limiting equation. To the best of our knowledge, this paper is the first study dealing with the study of concentrating solutions for Davey–Stewartson systems. We emphasize that with respect to the classical Schrödinger equation, the presence of a singular integral operator in the Davey–Stewartson system forces the implementation of new ideas to obtain the existence of multi-peak solutions.

Download Full-text

Solving the double barrier reflected BSDEs via penalization method

Statistics & Probability Letters ◽

10.1016/j.spl.2015.12.003 ◽

2016 ◽

Vol 110 ◽

pp. 74-83 ◽

Cited By ~ 2

Author(s):

Min Li ◽

Yufeng Shi

Keyword(s):

Double Barrier ◽

Penalization Method ◽

Reflected Bsdes

Download Full-text

A Semi-Langrangian Vortex Penalization Method for 3D Incompressible Flows

Journal of Mathematical Study ◽

10.4208/jms.v52n3.19.04 ◽

2019 ◽

Vol 52 (3) ◽

pp. 277-298

Author(s):

Chlo Mimeau sci

Keyword(s):

Incompressible Flows ◽

Penalization Method

Download Full-text

Backward Stochastic Differential Equations Driven by G-Brownian Motion with Double Reflections

Journal of Theoretical Probability ◽

10.1007/s10959-020-01038-5 ◽

2020 ◽

Author(s):

Hanwu Li ◽

Yongsheng Song

Keyword(s):

Brownian Motion ◽

Differential Equations ◽

Stochastic Differential Equations ◽

A Priori Estimates ◽

A Priori ◽

Backward Stochastic Differential Equations ◽

Penalization Method ◽

Priori Estimates ◽

Uniqueness And Existence

Abstract In this paper, we study the reflected backward stochastic differential equations driven by G-Brownian motion with two reflecting obstacles, which means that the solution lies between two prescribed processes. A new kind of approximate Skorohod condition is proposed to derive the uniqueness and existence of the solutions. The uniqueness can be proved by a priori estimates and the existence is obtained via a penalization method.

Download Full-text

Numerical simulation of bubbly flow around a cylinder by semi-Lagrangian–Lagrangian method

International Journal of Numerical Methods for Heat &amp Fluid Flow ◽

10.1108/hff-03-2019-0227 ◽

2019 ◽

Vol 29 (12) ◽

pp. 4660-4683 ◽

Cited By ~ 2

Author(s):

Van Luc Nguyen ◽

Tomohiro Degawa ◽

Tomomi Uchiyama ◽

Kotaro Takamure

Keyword(s):

Circular Cylinder ◽

Vortex Structure ◽

Bubbly Flow ◽

Three Dimensional ◽

Lagrangian Method ◽

Lagrangian Description ◽

Penalization Method ◽

Flow Around A Cylinder ◽

Content Type ◽

Flow Phenomena

Purpose The purpose of this study is to design numerical simulations of bubbly flow around a cylinder to better understand the characteristics of flow around a rigid obstacle. Design/methodology/approach The bubbly flow around a circular cylinder was numerically simulated using a semi-Lagrangian–Lagrangian method composed of a vortex-in-cell method for the liquid phase and a Lagrangian description of the gas phase. Additionally, a penalization method was applied to account for the cylinder inside the flow. The slip condition of the bubbles on the cylinder’s surface was enforced, and the outflow conditions were applied to the liquid flow at the far field. Findings The simulation clarified the characteristics of a bubbly flow around a circular cylinder. The bubbles were shown to move around and separate from both sides of the cylinder, because of entrainment by the liquid shear layers. Once the bubbly flow fully developed, the bubbles distributed into groups and were dispersed downstream of the cylinder. A three-dimensional vortex structure of various scales was also shown to form downstream, whereas a quasi-stable two-dimensional vortex structure was observed upstream. Overall, the proposed method captured the characteristics of a bubbly flow around a cylinder well. Originality/value A semi-Lagrangian–Lagrangian approach was applied to simulate a bubbly flow around a circular cylinder. The simulations provided the detail features of these flow phenomena.

Download Full-text

BSDE with rcll reflecting barrier driven by a Lévy process

Random Operators and Stochastic Equations ◽

10.1515/rose-2020-2029 ◽

2020 ◽

Vol 28 (1) ◽

pp. 63-77 ◽

Cited By ~ 1

Author(s):

Mohamed El Jamali ◽

Mohamed El Otmani

Keyword(s):

Differential Equation ◽

Stochastic Differential Equation ◽

Existence And Uniqueness ◽

Lévy Process ◽

Backward Stochastic Differential Equation ◽

American Option ◽

Levy Process ◽

Fair Price ◽

Penalization Method ◽

Uniqueness Of A Solution

AbstractIn this paper, we study the solution of a backward stochastic differential equation driven by a Lévy process with one rcll reflecting barrier. We show the existence and uniqueness of a solution by means of the penalization method when the coefficient is stochastic Lipschitz. As an application, we give a fair price of an American option.

Download Full-text