Focusing on fluid mechanics, this Research Note compiles mathematical studies on non-Newtonian and viscoelastic fluids, along with analyses of the Navier-Stokes equations in unbounded domains. It reviews both incompressible and compressible flow dynamics, as well as stability in magnetohydrodynamic and electrohydrodynamic contexts. The proceedings from a 1991 summer course in Lisbon offer a comprehensive survey and advanced introduction to fluid mechanics and partial differential equations, addressing a range of related topics.
This book consists of contributions originating from a conference in Obedo, Portugal, which honored the 70th birthday of V. A. Solonnikov. A broad variety of topics centering on nonlinear problems is presented, particularly Navier-Stokes equations, viscosity problems, diffusion-absorption equations, free boundaries, and Euler equations.
The book covers a range of topics related to phase changes, Stefan problems, and miscellaneous mathematical issues. It begins with generalized phase changes, discussing internal constraints and constitutive laws, liquid-vapor phase change in porous media, and the Cahn-Hilliard model for phase separation kinetics. It also explores shape memory alloys and automatic control of thermomechanical phase transitions, alongside irreversible phase changes and phase change phenomena without sharp interfaces.
The second section revisits the Stefan problem, addressing aspects such as surface tension, singularities in one-dimensional cases with supercooling, and kinetic undercooling regularization. It further examines two-phase Stefan problems with feedback controls and local mesh refinements in two dimensions, concluding with a linearization approach for parabolic free boundary problems.
The final section presents miscellaneous problems, including externally induced dissipative collisions, optimal control of hemivariational inequality systems, and a mathematical formulation for generalized Hertz impact problems. It also touches on free boundary value problems in composite masonry structures and uniqueness in evolution problems with hysteresis, along with a diffusion problem featuring a gradient constraint. An author index is included for reference.
