Tiešās un inversās problēmas hiperboliskajam siltuma vadīšanas vienādojumam
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Latvijas Universitāte
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Abstract
Darbā ir apskatīts hiperboliskais siltuma vienādojums, kā rīks dažādu fizisku procesu aprakstīšanai. Tiek pieminēti dažādi fiziskie procesi, kuru aprakstīšanai izmanto hiperbolisko siltuma vienādojumu. Tiek parādītas pāris metodes dažu problēmu atrisinājuma iegūšanai
Īpaša uzmanība tiek pievērsta tērauda rūdīšanas procesam un inversās problēmas atrašanai, kura, mūsu gadījumā, reprezentējās, kā procesa ātrums sākuma momentā, kuru praktiski nav iespējams noteikt.
Darba mērķis ir apskatīt tērauda rūdīšanas procesu caur hiperbolisku siltuma vienādojumu un atrast problēmas inverso atrisinājumu
Atslēga vārdi: hiperboliskais siltuma vienādojums, konservatīvās viduvēšanas metode, Grīna funkcija, integrālvienādojumi
At the paper the hyperbolic heat equation, as the instrument of describing of some physical processes was investigated. There are some methods of process solving given in the paper The attention of the paper was paid to steel quenching process and to the discovering the solution of inverse problem, which represents as velocity of the process at the initial time. Practically, this parameter cannot be determined The aim of this paper is to discover the process of steel quenching by using the hyperbolic heat transfer equation and to define the inverse problem of this process. Key words: hyperbolic heat equation, conservative averaging method, Green function, integral equations.
At the paper the hyperbolic heat equation, as the instrument of describing of some physical processes was investigated. There are some methods of process solving given in the paper The attention of the paper was paid to steel quenching process and to the discovering the solution of inverse problem, which represents as velocity of the process at the initial time. Practically, this parameter cannot be determined The aim of this paper is to discover the process of steel quenching by using the hyperbolic heat transfer equation and to define the inverse problem of this process. Key words: hyperbolic heat equation, conservative averaging method, Green function, integral equations.