1. Homogenization of diffusion equation with scalar hysteresis operator
- Creator:
- Franců, Jan
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- hysteresis, Prandtl-Ishlinskii operator, material with periodic structure, nonlinear diffusion equation, and homogenization
- Language:
- English
- Description:
- The paper deals with a scalar diffusion equation c ut = (F[ux])x+f, where F is a Prandtl-Ishlinskii operator and c, f are given functions. In the diffusion or heat conduction equation the linear constitutive relation is replaced by a scalar Prandtl-Ishlinskii hysteresis spatially dependent operator. We prove existence, uniqueness and regularity of solution to the corresponding initial-boundary value problem. The problem is then homogenized by considering a sequence of equations of the above type with spatially periodic data cε and ηε when the spatial period ε tends to zero. The homogenized characteristics c∗ and η∗ are identified and the convergence of the corresponding solutions to the solution of the homogenized equation is proved.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public