Acta Applicandae Mathematicae
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On the Weak Convergence of Monge-Ampère Measures for Discrete Convex Mesh Functions
Acta Applicandae Mathematicae - Tập 172 - Trang 1-31 - 2021
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...
On Conservation Laws for the Toda Equations
Acta Applicandae Mathematicae - Tập 83 - Trang 175-182 - 2004
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.
An Explicit Formula for the Nonstationary Diffracted Wave Scattered on a NN-Wedge
Acta Applicandae Mathematicae - - 2015
Decomposition and Group Theoretic Characterization of Pairs of Inverse Relations of the Riordan Type
Acta Applicandae Mathematicae - Tập 85 - Trang 93-109 - 2005
A new solution to Riordan’s problem of combinatorial identities classification
is presented. An algebgraic characterization of pairs of inverse relations of
the Riordan type is given. The use of the integral representation approach for
generating new types of combinatorial identities is demonstrated.
Regularity and Convergence Results of the Velocity-Vorticity-Voigt Model of the 3D Boussinesq Equations
Acta Applicandae Mathematicae - Tập 176 - Trang 1-25 - 2021
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...
An update on orthogonal polynomials and weighted approximation on the real line
Acta Applicandae Mathematicae - Tập 33 - Trang 121-164 - 1993
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...
On a Pump
Acta Applicandae Mathematicae - Tập 88 - Trang 125-141 - 2005
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...
Instability and Bifurcation in a Trend Depending Price Formation Model
Acta Applicandae Mathematicae - Tập 144 Số 1 - Trang 121-136 - 2016
Existence and Asymptotic Behavior of Solutions for the Unstirred Chemostat Model with Ratio-Dependent Function
Acta Applicandae Mathematicae - Tập 166 - Trang 223-232 - 2019
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...
Global Dynamics of Froude-Type Oscillators with Superlinear Damping Terms
Acta Applicandae Mathematicae - Tập 130 - Trang 81-113 - 2013
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 (x′)=|x′| r−2 x′. This equation is a
generalization of nonlinear ship rolling motion with Froude’s expression, which
is very familiar in marine eng...
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