Abstract
We consider a system of nonlinear parabolic PDEs which includes a constraint on the time-derivative depending on the unknowns. This system is a mathematical model for irreversible phase transitions. In our phase transition model, the constraint p := p(θ, w) is a function of the temperature θ and the order parameter (state variable) w and it is imposed on the velocity of the order parameter, for instance, in such a way that p(θ, w) ≤ w t ≤ p(θ, w) + (a positive constant). We give an existence result of the problem.
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© 2006 Birkhäuser Verlag Basel/Switzerland
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Aso, M., Frémond, M., Kenmochi, N. (2006). Parabolic Systems with the Unknown Dependent Constraints Arising in Phase Transitions. In: Figueiredo, I.N., Rodrigues, J.F., Santos, L. (eds) Free Boundary Problems. International Series of Numerical Mathematics, vol 154. Birkhäuser, Basel. https://doi.org/10.1007/978-3-7643-7719-9_5
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DOI: https://doi.org/10.1007/978-3-7643-7719-9_5
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