OPTIMAL CONTROL OF A CLASS OF NONLINEAR HEAT CONDUCTION MODELS

Menezes D, Límaco J (2026)

Publication Type: Journal article

Publication year: 2026

Journal

Evolution Equations and Control Theory American Institute of Mathematical Sciences (AIMS)

Book Volume: 26

Pages Range: 1-38

DOI: 10.3934/eect.2026094

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.

Involved external institutions

Federal Rural University of Semi-Árido (UFERSA) / Universidade Federal Rural do Semi-Árido (UFERSA) BR Brazil (BR) Fluminense Federal University / Universidade Federal Fluminense (UFF) BR Brazil (BR)

How to cite

APA:

Menezes, D., & Límaco, J. (2026). OPTIMAL CONTROL OF A CLASS OF NONLINEAR HEAT CONDUCTION MODELS. Evolution Equations and Control Theory, 26, 1-38. https://doi.org/10.3934/eect.2026094

MLA:

Menezes, Denilson, and Juan Límaco. "OPTIMAL CONTROL OF A CLASS OF NONLINEAR HEAT CONDUCTION MODELS." Evolution Equations and Control Theory 26 (2026): 1-38.

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