PreprintarXiv licencearXiv
Energy Estimate and Convergence of Weak Solutions of a Class of Nonlinear PDEs with Robin Boundary Conditions
Abstract
We establish strong convergence in L2([0,T]×[0,1]) of weak solutions to a class of nonlinear PDEs with Robin boundary conditions to weak solutions of the corresponding Neumann and Dirichlet problems as the boundary parameter κ tends to $0$ and ∞, respectively. Our approach relies on a particle system whose hydrodynamic limits yield the Robin problem for each fixed κ>0. An energy estimate derived from the microscopic stochastic dynamics provides the key bounds for passing to the subsequent limits κ→0 and κ→∞, thereby obtaining the Neumann and Dirichlet problems.
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BibTeX
@misc{neumann2026energy,
title = {{Energy Estimate and Convergence of Weak Solutions of a Class of Nonlinear PDEs with Robin Boundary Conditions}},
author = {Adriana Neumann and Patrícia Gonçalves and Maria Chiara Ricciuti and Oslenne Araújo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.25543},
eprint = {2610.25543},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.25543},
}
RIS
TY - UNPB
TI - Energy Estimate and Convergence of Weak Solutions of a Class of Nonlinear PDEs with Robin Boundary Conditions
AU - Adriana Neumann
AU - Patrícia Gonçalves
AU - Maria Chiara Ricciuti
AU - Oslenne Araújo
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.25543
UR - https://arxiv.org/abs/2610.25543
AB - We establish strong convergence in L^2([0,T]×[0,1]) of weak solutions to a class of nonlinear PDEs with Robin boundary conditions to weak solutions of the corresponding Neumann and Dirichlet problems as the boundary parameter κ tends to $0$ and ∞, respectively. Our approach relies on a particle system whose hydrodynamic limits yield the Robin problem for each fixed κ>0. An energy estimate derived from the microscopic stochastic dynamics provides the key bounds for passing to the subsequent limits κ→0 and κ→∞, thereby obtaining the Neumann and Dirichlet problems.
ER -