101 research outputs found
Regularity results for a class of obstacle problems under non standard growth conditions
We prove regularity results for minimizers of functionals F(u, Ω) := â«Î© f(x, u, Du) dx in the class K := {u â W1,p(x)(Ω, R) : u â„ Ï}, where Ï : Ω â R is a fixed function and f is quasiconvex and fulfills a growth condition of the type Lâ1|z|p(x) †f(x, Ο, z) †L(1 + |z|p(x)), with growth exponent p : Ω â (1, â)
An existence result for A P.D.E. with hysteresis, convection and a nonlinear boundary condition
In this paper a partial diïŹerential equation containing a continuous hysteresis operator and a convective term is considered. This model equation, which appears in the context of magnetohydrodynamics, is coupled with a nonlinear boundary condition containing a memory operator. Under suitable assumptions, an existence result is achieved using an implicit time discretization scheme
On a non-isothermal diffuse interface model for two-phase flows of incompressible fluids
We introduce a diffuse interface model describing the evolution of a mixture
of two different viscous incompressible fluids of equal density. The main
novelty of the present contribution consists in the fact that the effects of
temperature on the flow are taken into account. In the mathematical model, the
evolution of the macroscopic velocity is ruled by the Navier-Stokes system with
temperature-dependent viscosity, while the order parameter representing the
concentration of one of the components of the fluid is assumed to satisfy a
convective Cahn-Hilliard equation. The effects of the temperature are
prescribed by a suitable form of the heat equation. However, due to quadratic
forcing terms, this equation is replaced, in the weak formulation, by an
equality representing energy conservation complemented with a differential
inequality describing production of entropy. The main advantage of introducing
this notion of solution is that, while the thermodynamical consistency is
preserved, at the same time the energy-entropy formulation is more tractable
mathematically. Indeed, global-in-time existence for the initial-boundary value
problem associated to the weak formulation of the model is proved by deriving
suitable a-priori estimates and showing weak sequential stability of families
of approximating solutions.Comment: 26 page
Existence of solutions to a two-dimensional model for nonisothermal two-phase flows of incompressible fluids
We consider a thermodynamically consistent diffuse interface model describing
two-phase flows of incompressible fluids in a non-isothermal setting. This
model was recently introduced in a previous paper of ours, where we proved
existence of weak solutions in three space dimensions. Here, we aim at studying
the mathematical properties of the model in the two-dimensional case. In
particular, we can show existence of global in time strong solutions. Moreover,
we can admit slightly more general conditions on some material coefficients of
the system
Asymptotic behavior of a Neumann parabolic problem with hysteresis
A parabolic equation in two or three space variables with a Preisach hysteresis operator and with homogeneous Neumann boundary conditions is shown to admit a unique global regular solution. A detailed investigation of the Preisach memory dynamics shows that the system converges to an equilibrium in the state space of all admissible Preisach memory configurations as time tends to infinity
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