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April 16, 2026Nonlinear EngineeringOpen Access

Existence and uniqueness results of solutions for a new class of parabolic varitional inequalities related with impulse control problem

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Authors

SBSalah BoulaarasRGRafik GuefaifiaMHMohamed Haiour

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Overview

Novel framework demonstrates existence and uniqueness in parabolic quasi-variational inequalities, indicating practical advancements in impulse control problems.

Key Points

  • The study aims to establish existence and uniqueness results for new parabolic quasi-variational inequalities related to impulse control problems.
  • Developed a four-phase numerical framework for PQVIs.
  • Used finite element methods (FEM) for spatial discretization.
  • Implemented a semi-implicit time-stepping scheme for stability.
  • Created a discrete iterative algorithm linked to a fixed-point formulation.
  • Conducted a convergence analysis that extends classical results to the FEM setting.
  • Demonstrated existence and uniqueness of solutions for the proposed inequalities.
  • Showed improved stability and convergence for the numerical framework.
  • Derived refined error estimates in Sobolev norms under regularity assumptions.

Cite This Study

Boulaaras et al. (2026) studied this question.

synapsesocial.com/papers/69e07cc02f7e8953b7cbdeb9https://doi.org/10.1515/nleng-2025-0196
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