### Pavel Krejčí turns sixty and receives the Bernard Bolzano Honorary Medal for Merit in Mathematical Sciences

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Phase-field systems as mathematical models for phase transitions have drawn a considerable attention in recent years. However, while they are suitable for capturing many of the experimentally observed phenomena, they are only of restricted value in modelling hysteresis effects occurring during phase transition processes. To overcome this shortcoming of existing phase-field theories, the authors have recently proposed a new approach to phase-field models which is based on the mathematical theory...

In this paper, we develop a thermodynamically consistent description of the uniaxial behavior of thermovisco-elastoplastic materials for which the total stress $\sigma $ contains, in addition to elastic, viscous and thermic contributions, a plastic component ${\sigma}^{p}$ of the form ${\sigma}^{p}(x,t)=\mathcal{P}[\epsilon ,\theta (x,t)](x,t)$. Here $\epsilon $ and $\theta $ are the fields of strain and absolute temperature, respectively, and ${\left\{\mathcal{P}[\xb7,\theta ]\right\}}_{\theta >0}$ denotes a family of (rate-independent) hysteresis operators of Prandtl-Ishlinskii type, parametrized by the absolute temperature. The system of momentum...

An existence result is proved for a nonlinear diffusion problem of phase-field type, consisting of a parabolic system of two partial differential equations, complemented by Neumann homogeneous boundary conditions and initial conditions. This system is meant to model two-species phase segregation on an atomic lattice under the presence of diffusion. A similar system has been recently introduced and analyzed in [3]. Both systems conform to the general theory developed in [5]: two parabolic PDEs, interpreted...

The paper is devoted to the analysis of an abstract evolution inclusion with a non-invertible operator, motivated by problems arising in nonlocal phase separation modeling. Existence, uniqueness, and long-time behaviour of the solution to the related Cauchy problem are discussed in detail.

In this paper we propose a time discretization of a system of two parabolic equations describing diffusion-driven atom rearrangement in crystalline matter. The equations express the balances of microforces and microenergy; the two phase fields are the order parameter and the chemical potential. The initial and boundary-value problem for the evolutionary system is known to be well posed. Convergence of the discrete scheme to the solution of the continuous problem is proved by a careful development...

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