Homogenization of heat equation with hysteresis

Homogenization of heat equation with hysteresis

Článek recenzovaný mimo WoS a Scopus

The contribution delas with heat equaition in the form (c u+W[u])_t=div(a.grad u)=f, where the functional operator W[u] is Prandtl-Ishlinskii hysteresis operator of play type characterized by a distribution function eta. The spatially dependent initial boundary value problem is studied. Proof of existence and uniqueness of the solution is omitted since the proof is a slightly modified proof by Brokate-Sprekels. The homogenization problem for this equation si studied. For eps->0, a sequence of problems of the above type with spatially eps-periodic coefficients c^eps, eta,^eps, a^eps si considered. The coefficients c^star,eta^star and a^star in the homogenized problem are identified and convergence of the corresponding solutions u^eps to u^star is proved.

The contribution delas with heat equaition in the form (c u+W[u])_t=div(a.grad u)=f, where the functional operator W[u] is Prandtl-Ishlinskii hysteresis operator of play type characterized by a distribution function eta. The spatially dependent initial boundary value problem is studied. Proof of existence and uniqueness of the solution is omitted since the proof is a slightly modified proof by Brokate-Sprekels. The homogenization problem for this equation si studied. For eps->0, a sequence of problems of the above type with spatially eps-periodic coefficients c^eps, eta,^eps, a^eps si considered. The coefficients c^star,eta^star and a^star in the homogenized problem are identified and convergence of the corresponding solutions u^eps to u^star is proved.

Prandtl-Ishlinskii operaor, Homogenization, Heat equation

FRANCŮ, J.

01.01.2003

0378-4754

MATHEMATICS AND COMPUTERS IN SIMULATION

61

3-5

Nizozemsko

591

7