This book primarily concerns quasilinear and semilinear elliptic and parabolic partial
differential equations, inequalities, and systems. The exposition leads the reader through the …

Micromagnetics is a continuum variational theory describing magnetization patterns in
ferromagnetic media. Its multiscale nature due to different inherent spatiotemporal physical …

Our work on rate-independent systems was stimulated by our search for evolutionary
material models for shape-memory alloys that are flexible enough to encompass nonlinear …

Piezoelectric actuators find extensive application in delivering precision motion in the
micrometer to nanometer range. The advantages of a broader range of motion, rapid …

Rate-independent systems occur as limit problems in many physical and mechanical
problems if the interesting time scales are much longer than the intrinsic time scales in the …

We propose a rate-independent, mesoscopic model for the hysteretic evolution of phase
transformations in shape-memory alloys. The model uses the deformation and phase …

We consider mechanical models which are driven by an external loading on a time scale
much slower than any internal time scale (like viscous relaxation times) but still much faster …

Introduction In mechanics, rate-independent evolutionary problems have always played an
important role, eg, in Coulomb friction or in perfect plasticity. The intrinsic nonsmoothness …

This work uses the energetic formulation of rate-independent systems that is based on the
stored-energy functionals E and the dissipation distance D. For sequences (E _k) _ k ∈ N …

We introduce a new energetic formulation for the inelastic rate-independent behavior of
standard generalized materials. This formulation is solely based on the classical elastic …