In this paper, we discuss the existence results for a class of nonlinear integrodifferential evolution inclusions with nonlocal initial conditions in Banach spaces. Our results are based on a fixed point theorem for condensing maps due to Martelli and the resolvent operators combined with approximation techniques.

We establish existence of partially regular weak solutions for the Landau-Lifshitz equation in three space dimensions for smooth initial data of finite Dirichlet energy. The construction is based on Ginzburg-Landau approximation. The new key ingredient is a nonlocal representation formula for the penalty term that permits to take advantage of the special trilinear structure of the limiting nonl...

We develop a simple model for coupling the pseudo-Goldstone bosons of QCD Or's, K's, -q) to quark fields. This nonlocal model incorporates a momentum dependent dynamical quark mass ,~ (p) in a manner consistent with global chiral symmetry. Explicit current quark masses and gauge fields are also introduced. All low energy parameters of the chiral lagrangian are expressed in terms of ~(p). In par...

A Helmholtz energy functional for inhomogeneous fluid phases based on the perturbed-chain polar statistical associating fluid theory (PCP-SAFT) equation of state is proposed. The model is supplemented with a capillary wave contribution to the surface tension to account for long-wavelength fluctuations of a vapor-liquid interface. The functional for the dispersive attraction is based on a nonloc...

We investigate the behavior of three-dimensional (3D) exchange-correlation energy functional approximations of density functional theory in anisotropic systems with two-dimensional (2D) character. Using two simple models, quasi-2D electron gas and two-electron quantum dot, we show a fundamental limitation of the local density approximation (LDA), and its semi-local extensions, generalized gradi...

We solve the long-standing problem of the large overestimation of the static polarizability of conjugated polymers obtained using the local density approximation within density-functional theory. The local approximation is unable to describe the highly nonlocal exchange and correlation (xc) effects found in these quasi-one-dimensional systems. Time-dependent current-density-functional theory en...

The surface impedance approach is discussed in connection with the precise calculation of the Casimir force between metallic plates. It allows us to take into account the nonlocal connection between the current density and electric field inside of metals. In general, a material has to be described by two impedances Zssv ,qd and Zpsv ,qd corresponding to two different polarization states. In con...

We analyze coherent structures in nonlocal dispersive active-dissipative nonlinear systems, using as a prototype the Kuramoto–Sivashinsky (KS) equation with an additional nonlocal term that contains stabilizing/destabilizing and dispersive parts. As for the local generalized Kuramoto–Sivashinsky (gKS) equation (see, e.g., [T. Kawahara and S. Toh, Phys. Fluids, 31 (1988), pp. 2103–2111]), we sho...