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arXiv · 2608.18896

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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Denilson Menezes, Juan Límaco. 2026-08-19. Optimal control of a class of nonlinear heat conduction models. https://arxiv.org/abs/2608.18896

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