-widths for singularly perturbed problems
-widths for singularly perturbed problems
Kolmogorov -widths are an approximation theory concept that, for a given problem, yields information about the optimal rate of convergence attainable by any numerical method applied to that problem. We survey sharp bounds recently obtained for the -widths of certain singularly perturbed convection-diffusion and reaction-diffusion boundary value problems.
Navier–Stokes regularization of multidimensional Euler shocks
Nearly concentric Korteweg-de Vries equation and periodic traveling wave solution.
Neue Kriterien für das Fehlen von L2-Lösungen für -...v = f(x, v) im Rn unter besonderer Berücksichtigung des linearen Falles.
Neumann problem for one-dimensional nonlinear thermoelasticity
The global existence theorem of classical solutions for one-dimensional nonlinear thermoelasticity is proved for small and smooth initial data in the case of a bounded reference configuration for a homogeneous medium, considering the Neumann type boundary conditions: traction free and insulated. Moreover, the asymptotic behaviour of solutions is investigated.
Neumann problem in a class of harmonic functions in domains with a piecewise-Lyapunov boundary.
New a priori estimates for nondiagonal strongly nonlinear parabolic systems
We consider nondiagonal elliptic and parabolic systems of equations with quadratic nonlinearities in the gradient. We discuss a new description of regular points of solutions of such systems. For a class of strongly nonlinear parabolic systems, we estimate locally the Hölder norm of a solution. Instead of smallness of the oscillation, we assume local smallness of the Campanato seminorm of the solution under consideration. Theorems about quasireverse Hölder inequalities proved by the author are essentially...
New a priori estimates for -nonlinear elliptic systems with strong nonlinearities in the gradient, .
New and old function spaces in the theory of PDEs and nonlinear analysis
New characterizations of asymptotic stability for evolution families on Banach spaces.
New estimates for div-curl products and very weak solutions of PDEs
New exact solutions for the -dimensional Broer-Kaup-Kupershmidt equations.
New existence and stability results for partial fractional differential inclusions with multiple delay
We discuss the existence of solutions and Ulam's type stability concepts for a class of partial functional fractional differential inclusions with noninstantaneous impulses and a nonconvex valued right hand side in Banach spaces. An example is provided to illustrate our results.
New isoperimetric estimates for solutions to Monge-Ampère equations
New Liouville theorems for linear second order degenerate elliptic equations in divergence form
New optimal regularity results for infinite-dimensional elliptic equations
In questo articolo si ottengono stime di Schauder di tipo nuovo per equazioni ellittiche infinito-dimensionali del secondo ordine con coefficienti Hölderiani a valori nello spazio degli operatori Hilbert-Schmidt. In particolare si mostra che la derivata seconda delle soluzioni è Hilbert-Schmidt.
New regularity results for a generic model equation in exterior 3D domains
We consider a generic scalar model for the Oseen equations in an exterior three-dimensional domain. We assume the case of a non-constant coefficient function. Using a variational approach we prove new regularity properties of a weak solution whose existence and uniqueness in anisotropically weighted Sobolev spaces were proved in [10]. Because we use some facts and technical tools proved in the above mentioned paper, we give also a brief review of its results and methods.
New solutions of equations on
New spectral criteria for almost periodic solutions of evolution equations
We present a general spectral decomposition technique for bounded solutions to inhomogeneous linear periodic evolution equations of the form ẋ = A(t)x + f(t) (*), with f having precompact range, which is then applied to find new spectral criteria for the existence of almost periodic solutions with specific spectral properties in the resonant case where may intersect the spectrum of the monodromy operator P of (*) (here sp(f) denotes the Carleman spectrum of f). We show that if (*) has a bounded...