Homogenization for a Volterra Equation.
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WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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Nonlinear heat flow in a heterogeneous material is considered. In this model, the internal genergy and heat flux depend upon the history of the temperature and the gradient of the temperature respectively. The heat conservation law leads to a Nonlinear Volterra integrodifferential equation with appropriate boundary conditions. This problem is solved under physically reasonable assumptions and its homogenization is investigated introducing a small parameter beta measuring the tightness of the heterogeneity of the medium typically we assume beta-periodicity for the physical parameters, the stability of the model is studied as beta goes to zero and the homogenized ideal limit medium is characterized in some cases, including the linear one. Author
- Numerical Mathematics