Related papers: Local and global smoothing effects for some linear…
We study a model of rolling particles subject to stochastic fluctuations, which may be relevant in systems of nano- or micro-scale particles where rolling is an approximation for strong static friction. We consider the simplest possible…
A huge number of technological and biological systems involves the lubricated contact between rough surfaces of soft solids in relative accelerated motion. Examples include dynamical rubber seals and the human joints. In this study we…
We study smoothness of generalized solutions of nonlocal elliptic problems in plane bounded domains with piecewise smooth boundary. The case where the support of nonlocal terms can intersect the boundary is considered. We announce…
We study local regularity properties for solutions of linear, non-uniformly elliptic equations. Assuming certain integrability conditions on the coefficient field, we prove local boundedness and Harnack inequality. The assumed integrability…
We are concerned with a model describing the motion of two compressible, immiscible fluids with density-dependent viscosity in the whole $\mathbb R^3$. The phases of the flow may have different pressure and viscosity laws and are separated…
We consider the 2D quasi-geostrophic equation with supercritical dissipation and dispersive forcing in the whole space. When the dispersive amplitude parameter is large enough, we prove the global well-posedness of strong solution to the…
The response to a localized force provides a sensitive test for different models of stress transmission in granular solids. The elasto-plastic models traditionally used by engineers have been challenged by theoretical and experimental…
A linear system of differential equations describing a joint motion of thermoelastic porous body and thermofluid occupying porous space is considered. Although the problem is linear, it is very hard to tackle due to the fact that its main…
We generalize the oscillator model of a particle interacting with a thermal reservoir by introducing arbitrary nonlinear couplings in the particle coordinates.The equilibrium positions of the heat bath oscillators are promoted to space-time…
The existence and multiplicity of solutions for a class of non-local elliptic boundary value problems with superlinear source functions are investigated in this paper. Using variational methods, we examine the changes arise in the solution…
In this paper we study the homogenization effects on the model of elastic plate in the bending regime, under the assumption that the energy density (material) oscillates in the direction of thickness. We study two different cases. First, we…
We study the two-dimensional (2D) shear flow of amorphous solids within variants of an elastoplastic model, paying particular attention to spatial correlations and time fluctuations of, e.g., local stresses. The model is based on the local…
We investigate both numerically and analytically the effect of strong disorder on the large scale properties of the hyperbolic equations for stresses proposed in \protect\cite{bcc,wcc}. The physical mechanism that we model is the local…
We investigate phase separation including elastic coherency effects in the bulk and at surfaces and find a reduction of the solubility limit in the presence of free surfaces. This mechanism favours phase separation near free surfaces even…
This work explores the solvability of a sixth-order Cahn--Hilliard equation with an inertial term, which serves as a relaxation of a higher-order variant of the classical Cahn--Hilliard equation. The equation includes a source term that…
We deal with the regularity problem for linear, second order parabolic equations and systems in divergence form with measurable data over non-smooth domains, related to variational problems arising in the modeling of composite materials and…
This paper considers a family of second-order periodic parabolic equations with highly oscillating potentials, which have been considered many times for the time-varying potentials in stochastic homogenization. Following a standard…
We study the well-posedness for initial boundary value problems associated with time fractional diffusion equations with non-homogenous boundary and initial values. We consider both weak and strong solutions for the problems. For weak…
Piecewise smooth dynamical systems make use of discontinuities to model switching between regions of smooth evolution. This introduces an ambiguity in prescribing dynamics at the discontinuity: should it be given by a limiting value on one…
This work develops a dynamic homogenization approach for metamaterials. It finds an approximate macroscopic homogenized equation with constant coefficients posed in space and time; however, the resulting homogenized equation is higher order…