Nonlocal problems for the equations of motion of Kelvin-Voigt fluids
Nonlocal quadratic evolution problems
Nonlinear nonlocal parabolic equations modeling the evolution of density of mutually interacting particles are considered. The inertial type nonlinearity is quadratic and nonlocal while the diffusive term, also nonlocal, is anomalous and fractal, i.e., represented by a fractional power of the Laplacian. Conditions for global in time existence versus finite time blow-up are studied. Self-similar solutions are constructed for certain homogeneous initial data. Monte Carlo approximation schemes by interacting...
Nonlocal quasilinear damped differential inclusions.
Nonlocal Robin problem for elliptic second order equations in a plane domain with a boundary corner point
We investigate the behavior of weak solutions to the nonlocal Robin problem for linear elliptic divergence second order equations in a neighborhood of a boundary corner point. We find an exponent of the solution's decreasing rate under minimal assumptions on the problem coefficients.
Nonlocal symmetries and generation of solutions for partial differential equations.
Nonlocal variational problems arising in long wave propagation
Nonlocal variational problems arising in long wave propagatioN
In this paper we study the existence of minimizer for certain constrained variational problems given by functionals with nonlocal terms. This type of functionals are first integrals of evolution equations describing long wave propagation and the existence of minimizer gives the existence and the stability of traveling waves for these equations. Due to loss of compactness, the major problem is to prevent dichotomy of minimizing sequences. Our approach is an alternative to the concentration-compactness...
Non-Markovian quadratic forms obtained by homogenization
This paper is devoted to the asymptotic behaviour of quadratic forms defined on . More precisely we consider the -convergence of these functionals for the -weak topology. We give an example in which some limit forms are not Markovian and hence the Beurling-Deny representation formula does not hold. This example is obtained by the homogenization of a stratified medium composed of insulating thin-layers.
Non-negative solutions of generalized porous medium equations.
The purpose of this paper is to study nonnegative solutions u of the nonlinear evolution equations∂u/∂t = Δφ(u), x ∈ Rn, 0 < t < T ≤ +∞ (1.1)Here the nonlinearity φ is assumed to be continuous, increasing with φ(0) = 0. This equation arises in various physical problems, and specializing φ leads to models for nonlinear filtrations, or for the gas flow in a porous medium. For a recent survey in these equations see [9].The main object of this work is to study the initial value problem...
Non-negative solutions of linear parabolic equations : an addendum
Nonnegative solutions of parabolic operators with low-order terms.
Non-negative solutions to fast diffusions.
The purpose of this work is to study the class of non-negative continuous weak solutions of the non-linear evolution equation∂u/∂t = ∆φ(u), x ∈ Rn, 0 < t < T ≤ +∞.
Non-Newtonian fluids and function spaces
In this note we give an overview of recent results in the theory of electrorheological fluids and the theory of function spaces with variable exponents. Moreover, we present a detailed and self-contained exposition of shifted -functions that are used in the studies of generalized Newtonian fluids and problems with -structure.
Nonoscillation theorems for a class of neutral functional differential equations of arbitrary order
Nonparametric minimal surfaces in whose boundaries have a jump discontinuity.
Non-periodic solutions to relativistic field equations : hyperbolic case
Non-planar fronts in Boussinesq reactive flows
Nonradial solutions of nonlinear Neumann problems in radially symmetric domains
Non-Realizable CR Structures.
Nonreflecting Boundary Conditions for Hyperbolic Conservation laws