Field patterns occur in space–time microstructures such that a disturbance propagating
along a characteristic line does not evolve into a cascade of disturbances, but rather …

We consider a two-phase isotropic optimal design problem within the context of the transient
heat equation. The objective is to minimize the average of the dissipated thermal energy …

A space–time extension of the topology optimization method is presented. The formulation,
with design variables in both the spatial and temporal domains, is used to create structures …

The goal of this work is to improve focusing of high-intensity ultrasound by modifying the
geometry of acoustic lenses through shape optimization. The shape optimization problem is …

We consider the heat equation in (0, T)× Ω, Ω⊂ RN, N⩾ 1, and address the nonlinear
optimal design problem which consists in finding the distribution in Ω of two given isotropic …

We consider a linear damped wave equation defined on a two-dimensional domain Ω, with
a dissipative term localized in a subset ω. We address the shape design problem which …

An algorithm is proposed to optimize the performance of multiphase structures (composites)
under elastodynamic loading conditions. The goal is to determine the distribution of material …

In the framework of the linear fracture theory, a commonly-used tool to describe the smooth
evolution of a crack embedded in a bounded domain Ω is the so-called energy release rate …

This paper considers the problem of controlling the solution of an initial boundary‐value
problem for a wave equation with time‐dependent sound speed. The control problem is to …

An optimal design problem governed by the wave equation is examined in detail.
Specifically, we seek the time-dependent optimal layout of two isotropic materials on a 1-d …