Nonanalytic solutions of the KdV equation.
Nonanalyticity of solutions to
It is proved that the solution to the initial value problem , u(0,x) = 1/(1+x²), does not belong to the Gevrey class in time for 0 ≤ s < 1. The proof is based on an estimation of a double sum of products of binomial coefficients.
Non-autonomous 2D Navier–Stokes system with a simple global attractor and some averaging problems
We study the global attractor of the non-autonomous 2D Navier–Stokes system with time-dependent external force . We assume that is a translation compact function and the corresponding Grashof number is small. Then the global attractor has a simple structure: it is the closure of all the values of the unique bounded complete trajectory of the Navier–Stokes system. In particular, if is a quasiperiodic function with respect to , then the attractor is a continuous image of a torus. Moreover the...
Non-autonomous 2D Navier–Stokes system with a simple global attractor and some averaging problems
We study the global attractor of the non-autonomous 2D Navier–Stokes system with time-dependent external force g(x,t). We assume that g(x,t) is a translation compact function and the corresponding Grashof number is small. Then the global attractor has a simple structure: it is the closure of all the values of the unique bounded complete trajectory of the Navier–Stokes system. In particular, if g(x,t) is a quasiperiodic function with respect to t, then the attractor is a continuous image...
Non-autonomous stochastic Cauchy problems in Banach spaces
We study the non-autonomous stochastic Cauchy problem on a real Banach space E, , t ∈ [0,T], U(0) = u₀. Here, is a cylindrical Brownian motion on a real separable Hilbert space H, are closed and densely defined operators from a constant domain (B) ⊂ H into E, denotes the generator of an evolution family on E, and u₀ ∈ E. In the first part, we study existence of weak and mild solutions by methods of van Neerven and Weis. Then we use a well-known factorisation method in the setting of evolution...
Nonautonomous ultraparabolic equations applied to population dynamics.
Noncharacteristic mixed problems for hyperbolic systems of the first order [Book]
Nonclassical approximate symmetries of evolution equations with a small parameter.
Non-classical phase transitions at a sonic point.
Nonclassical problems for the second order hyperbolic equations.
Nonclassical Riemann solvers and kinetic relations III: A nonconvex hyperbolic model for Van der Waals fluids.
Nonclassical shock waves of conservation laws: Flux function having two inflection points.
Noncoercive boundary value problems for the Lapace equation with a spectral parameter.
Nonconforming finite element approximations of the Steklov eigenvalue problem and its lower bound approximations
The paper deals with error estimates and lower bound approximations of the Steklov eigenvalue problems on convex or concave domains by nonconforming finite element methods. We consider four types of nonconforming finite elements: Crouzeix-Raviart, , and enriched Crouzeix-Raviart. We first derive error estimates for the nonconforming finite element approximations of the Steklov eigenvalue problem and then give the analysis of lower bound approximations. Some numerical results are presented to...
Nonconforming Finite Element Methods for Eigenvalue Problems in Linear Plate Theory.
Nonconforming Galerkin methods based on quadrilateral elements for second order elliptic problems
Nonconforming Galerkin methods based on quadrilateral elements for second order elliptic problems
Low-order nonconforming Galerkin methods will be analyzed for second-order elliptic equations subjected to Robin, Dirichlet, or Neumann boundary conditions. Both simplicial and rectangular elements will be considered in two and three dimensions. The simplicial elements will be based on P1, as for conforming elements; however, it is necessary to introduce new elements in the rectangular case. Optimal order error estimates are demonstrated in all cases with respect to a broken norm in H1(Ω)...
Non-constant positive steady states for a predator-prey cross-diffusion model with Beddington-DeAngelis functional response.
Nonconvex evolution inclusions generated by time-dependent subdifferential operators.
Non-convex perturbations of evolution equations with -dissipative operators in Banach spaces