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Stability of well-posed stochastic evolution equation.

S A Bishop1, S A Iyase1, H I Okagbue1

  • 1Department of Mathematics, Covenant University, Ota, Ogun State, Nigeria.

Heliyon
|December 18, 2019
PubMed
Summary
This summary is machine-generated.

This study examines the stability of stochastic evolution equations with impulsive and nonlocal conditions. We demonstrate that Ulam-type stability is achieved for these equations under specific mathematical conditions.

Keywords:
Evolution EquationImpulsive and nonlocal conditionsMathematicsStochastic processesUlams-Hyers stability

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Area of Science:

  • Stochastic Analysis
  • Nonlinear Dynamics
  • Differential Equations

Background:

  • Stochastic evolution equations are crucial for modeling complex systems.
  • Impulsive and nonlocal conditions introduce unique challenges in stability analysis.
  • Understanding well-posedness and stability is fundamental for practical applications.

Purpose of the Study:

  • To investigate the stability of non-classical stochastic evolution equations.
  • To analyze the impact of nonlocal initial conditions on solution properties.
  • To establish conditions for Ulam-type stability in this context.

Main Methods:

  • General perspective analysis of stochastic evolution equations.
  • Investigation of well-posedness and stability criteria.
  • Application of Ulam-type stability concepts.

Main Results:

  • The nonlocal conditions significantly influence the well-posedness and stability.
  • Ulam-type stability is proven to hold for the considered class of equations.
  • A supporting example illustrates the theoretical findings.

Conclusions:

  • Nonlocal conditions can be effectively managed to ensure stability.
  • The findings extend the understanding of stability for impulsive stochastic systems.
  • The research provides a theoretical framework and practical validation for Ulam-type stability.