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An Integrodifferential Equation Arising in Thermo‐Viscoelasticity
Author(s) -
Weinitschke H. J.
Publication year - 1984
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm198471179
Subject(s) - viscoelasticity , thermal conduction , heat equation , viscosity , mathematical analysis , spheres , mathematics , simple (philosophy) , volterra integral equation , physics , mechanics , thermodynamics , classical mechanics , integral equation , philosophy , epistemology , astronomy
Viscoelastic material at high temperature is subjected to a cooling process. The stresses built up in the body are determined from a system of equations containing a strongly temperature‐dependent viscosity η ( T ), where the temperature T is given by the heat conduction equation. It is shown that for simple geometries such as infinite cylinders and spheres, the basic equations can be reduced to a single Volterra‐type integrodifferential equation, which is shown to have a unique solution.
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