Viscosity Solution of System of Integro-Partial Differential Equations with Interconnected Obstacles of Non-local Type Without Monotonicity Conditions

被引：1

作者：

Hamadene, Said ^{[1
]}

Mnif, Mohamed ^{[2
]}

Neffati, Sarra ^{[2
]}

机构：

[1] Le Mans Univ, LMM, Ave Olivier Messiaen, F-72085 Le Mans 9, France

[2] Univ Tunis El Manar, Lab Modelisat Math & Numer, ENIT, Tunis, Tunisia

来源：

JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS | 2023年 / 35卷 / 02期

关键词：

Integro-partial differential equations; Interconnected obstacles; Non-local terms; Viscosity solution; Switching problem; Reflected backward stochastic differential equations with jumps;

D O I：

10.1007/s10884-021-09957-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study a system of second order integro-partial differential equations with interconnected obstacles with non-local terms, related to an optimal switching problem with the jump-diffusion model. Getting rid of the monotonicity condition on the generators with respect to the jump component, we construct a continuous viscosity solution which is unique in the class of functions with polynomial growth. In our study, the main tool is the associated of reflected backward stochastic differential equations with jumps with interconnected obstacles for which we show the existence of a unique Markovian solution.

引用

页码：1151 / 1173

页数：23

共 14 条

[1] Viscosity Solution of System of Integro-Partial Differential Equations with Interconnected Obstacles of Non-local Type Without Monotonicity Conditions
Said Hamadène
Mohamed Mnif
Sarra Neffati
Journal of Dynamics and Differential Equations, 2023, 35 : 1151 - 1173
[2] Viscosity Solutions of Systems of Variational Inequalities with Interconnected Bilateral Obstacles of Non-Local Type
Hamadene, Said
Zhao, Xuzhe
JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 2018, 30 (04) : 1731 - 1756
[3] Regularity properties of viscosity solutions of integro-partial differential equations of Hamilton-Jacobi-Bellman type
Jing, Shuai
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2013, 123 (02) : 300 - 328
[4] Viscosity Solutions of Systems of Variational Inequalities with Interconnected Bilateral Obstacles of Non-Local Type
Said Hamadène
Xuzhe Zhao
Journal of Dynamics and Differential Equations, 2018, 30 : 1731 - 1756
[5] Analytical and numerical solution techniques for a class of time-fractional integro-partial differential equations
Maji, Sandip
Natesan, Srinivasan
NUMERICAL ALGORITHMS, 2023, 94 (01) : 229 - 256
[6] Analytical and numerical solution techniques for a class of time-fractional integro-partial differential equations
Sandip Maji
Srinivasan Natesan
Numerical Algorithms, 2023, 94 : 229 - 256
[7] Viscosity solutions for second order integro-differential equations without monotonicity condition: the probabilistic approach
Hamadene, Said
Morlais, Marie-Amelie
STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES, 2016, 88 (04) : 632 - 649
[8] System of Nonlinear Second-Order Parabolic Partial Differential Equations with Interconnected Obstacles and Oblique Derivative Boundary Conditions on Non-Smooth Time-Dependent Domains
Jakani, Manal
APPLIED MATHEMATICS AND OPTIMIZATION, 2023, 88 (02)
[9] Viscosity solutions of second order integral-partial differential equations without monotonicity condition: A new result
Hamadene, Said
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2016, 147 : 213 - 235
[10] System of Nonlinear Second-Order Parabolic Partial Differential Equations with Interconnected Obstacles and Oblique Derivative Boundary Conditions on Non-Smooth Time-Dependent Domains
Manal Jakani
Applied Mathematics & Optimization, 2023, 88

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