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PreprintCC BY-NC-ND 4.0arXiv

Optimal control of a class of nonlinear heat conduction models

  • Denilson Menezes
  • Juan Límaco
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Abstract

We study an optimal control problem for a quasilinear parabolic equation modeling nonlinear heat conduction during heat treatment of metals. Under general assumptions, we prove existence of an optimal control and characterize the associated optimal control-state pair in a practically relevant framework. The main difficulty is the quadratic gradient term, which we handle through energy estimates and differentiability properties of the control-to-state map.

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Cite

BibTeXRIS
BibTeX
@misc{menezes2026optimal,
  title = {{Optimal control of a class of nonlinear heat conduction models}},
  author = {Denilson Menezes and Juan Límaco},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.18896},
  eprint = {2608.18896},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.18896},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Optimal control of a class of nonlinear heat conduction models
AU  - Denilson Menezes
AU  - Juan Límaco
PY  - 2026
DA  - 2026/08/19
PB  - arXiv
DO  - 10.48550/arxiv.2608.18896
UR  - https://arxiv.org/abs/2608.18896
AB  - We study an optimal control problem for a quasilinear parabolic equation modeling nonlinear heat conduction during heat treatment of metals. Under general assumptions, we prove existence of an optimal control and characterize the associated optimal control-state pair in a practically relevant framework. The main difficulty is the quadratic gradient term, which we handle through energy estimates and differentiability properties of the control-to-state map.
ER  -