On mathematical models with unknown nonlinear convection coefficients in one-phase heat transform processes

Nataliya Gol'dman; Nataliya Gol'dman

doi:10.3934/math.2019.2.327

AIMS Mathematics

2019, Volume 4, Issue 2: 327-342. doi: 10.3934/math.2019.2.327

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On mathematical models with unknown nonlinear convection coefficients in one-phase heat transform processes

Nataliya Gol'dman ^,

Science Research Computer Center, Moscow State University, Moscow 119992, Russia

Received: 29 January 2019 Accepted: 27 March 2019 Published: 11 April 2019

In this work, one-phase models for restoration of unknown temperature-dependent convection coefficients are considered by using the final observation of the temperature distribution and the phase boundary position. The proposed approach allows one to obtain sufficient conditions of unique identification of such coefficients in a class of smooth functions. Sets of admissible solutions preserving the uniqueness property are indicated. The considered mathematical models allow one to take into account the dependence of thermophysical characteristics upon the temperature. The work is connected with theoretical investigation of inverse Stefan problems for a parabolic equation with unknown coefficients. Such problems essentially differ from Stefan problems in the direct statements, where all the input data are given.
- one-phase models,
- inverse restoration problems,
- quasilinear parabolic equations,
- Stefan problems,
- uniqueness property
Citation: Nataliya Gol'dman. On mathematical models with unknown nonlinear convection coefficients in one-phase heat transform processes[J]. AIMS Mathematics, 2019, 4(2): 327-342. doi: 10.3934/math.2019.2.327

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Abstract

In this work, one-phase models for restoration of unknown temperature-dependent convection coefficients are considered by using the final observation of the temperature distribution and the phase boundary position. The proposed approach allows one to obtain sufficient conditions of unique identification of such coefficients in a class of smooth functions. Sets of admissible solutions preserving the uniqueness property are indicated. The considered mathematical models allow one to take into account the dependence of thermophysical characteristics upon the temperature. The work is connected with theoretical investigation of inverse Stefan problems for a parabolic equation with unknown coefficients. Such problems essentially differ from Stefan problems in the direct statements, where all the input data are given.

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