非局部分支过程的非线性Dirichlet问题

IF 1.2 3区数学 Q1 MATHEMATICS Journal of Mathematical Analysis and Applications Pub Date : 2025-07-01 Epub Date: 2025-01-20 DOI:10.1016/j.jmaa.2025.129281

Lucian Beznea , Oana Lupaşcu-Stamate , Alexandra Teodor

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引用次数: 0

摘要

提出了一种求解具有不连续边界数据的非线性Dirichlet问题的方法，并利用与算子的非线性项相关的非局部分支过程给出了解的概率表示。对于给定的边界数据，我们使用允许边界不连续的控制收敛来代替解的逐点收敛。

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Nonlinear Dirichlet problem of non-local branching processes

We present a method of solving a nonlinear Dirichlet problem with discontinuous boundary data and we give a probabilistic representation of the solution using the non-local branching process associated with the nonlinear term of the operator. Instead of the pointwise convergence of the solution to the given boundary data we use the controlled convergence which allows to have discontinuities at the boundary.

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来源期刊

Journal of Mathematical Analysis and Applications 数学-数学

CiteScore

2.50

自引率

7.70%

发文量

790

审稿时长

6 months

期刊介绍： The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Papers are sought which employ one or more of the following areas of classical analysis: • Analytic number theory • Functional analysis and operator theory • Real and harmonic analysis • Complex analysis • Numerical analysis • Applied mathematics • Partial differential equations • Dynamical systems • Control and Optimization • Probability • Mathematical biology • Combinatorics • Mathematical physics.