On the Weak Convergence of Monge-Ampère Measures for Discrete Convex Mesh FunctionsActa Applicandae Mathematicae - Tập 172 - Trang 1-31 - 2021
Gerard Awanou
To a mesh function we associate the natural analogue of the Monge-Ampère measure. The latter is shown to be equivalent to the Monge-Ampère measure of the convex envelope. We prove that the uniform convergence to a bounded convex function of mesh functions implies the uniform convergence on compact subsets of their convex envelopes and hence the weak convergence of the associated Monge-Ampère measu...... hiện toàn bộ
On Conservation Laws for the Toda EquationsActa Applicandae Mathematicae - Tập 83 - Trang 175-182 - 2004
Arthemy V. Kiselev
A description of the two-dimensional Toda equations' Noether symmetries, assigned to conservation laws for the latter equations, is given. A continuum of recursion operators, both local and nonlocal, is obtained for the Toda equations' symmetry algebras.
Regularity and Convergence Results of the Velocity-Vorticity-Voigt Model of the 3D Boussinesq EquationsActa Applicandae Mathematicae - Tập 176 - Trang 1-25 - 2021
Yuan Pei
We prove in this article for the first time for a multi-physical system: the 3D Boussinesq equations, the global well-posedness of the Voigt-regularized velocity-vorticity formulation model (VVVB), which attracts great interest from the numerical and computational study in fluid dynamics. We also obtain the higher-order regularity of the solution to the VVVB equations without regularizing the ther...... hiện toàn bộ
An update on orthogonal polynomials and weighted approximation on the real lineActa Applicandae Mathematicae - Tập 33 - Trang 121-164 - 1993
D. S. Lubinsky
We briefly review the state of orthogonal polynomials on (−∞, ∞), concentrating on analytic aspects, such as asymptotics and bounds on orthogonal polynomials, their zeros and their recurrence coefficients. We emphasize results rather than proofs. We also discuss applications to mean convergence of orthogonal expansions, Lagrange interpolation, Jackson-Bernstein theorems and the weighted “incomplet...... hiện toàn bộ
On a PumpActa Applicandae Mathematicae - Tập 88 - Trang 125-141 - 2005
Piotr Bogusław Mucha
We examine the Navier–Stokes equations in a two space dimensional time dependent domain. The system is considered with nonhomogeneous slip boundary conditions. The main result shows that under a certain geometrical constraint on deformations of the domain, it is possible to prove existence of solutions globally in time for arbitrary flows across the boundary with a new time independent bound on th...... hiện toàn bộ
Existence and Asymptotic Behavior of Solutions for the Unstirred Chemostat Model with Ratio-Dependent FunctionActa Applicandae Mathematicae - Tập 166 - Trang 223-232 - 2019
Wenbin Yang
A system of reaction-diffusion equations arising from the unstirred chemostat model with ratio-dependent function is considered. The asymptotic behavior of solutions is given and all positive steady-state solutions to this model lie on a single smooth solution curve. It turns out that the ratio-dependence effect will not affect the dynamics, compared with (Hsu and Waltman in SIAM J. Appl. Math. 53...... hiện toàn bộ
Global Dynamics of Froude-Type Oscillators with Superlinear Damping TermsActa Applicandae Mathematicae - Tập 130 - Trang 81-113 - 2013
Jitsuro Sugie, Takashi Yamasaki
This paper deals with the damped superlinear oscillator
$$x'' + a(t)\phi_p\bigl(x' \bigr) + b(t)\phi_q\bigl(x'\bigr)+ \omega^2x = 0, $$
where a(t) and b(t) are continuous and nonnegative for t≥0; p and q are real numbers greater than or equal to 2; ϕ
r
(...... hiện toàn bộ