Acta Applicandae Mathematicae: an international survey journal on applying mathematics and mathematical applications

Recently 3D image processing has interested researchers in both theoretical and applied fields and thus has constituted a challenging subject. Theoretically, this needs suitable functional bases that are easy to implement by the next. It holds ...

This the first time that the problem of global asymptotic stability analysis, and mixed $H_{\mathrm{\infty }}$ and passive control for a class of control fractional-order nonlinear systems has been studied in this paper. By using the Lyapunov direct method and some ...${}_{\mathrm{}}$${}_{\mathrm{}}$$\mathrm{}\mathrm{}$

By the flux-approximation method, we study limits of Riemann solutions to the Brio system with two independent parameters. The Riemann problem of the perturbed system is solved analytically, and four kinds of solutions are obtained constructively. ...

In this paper, we prove transportation inequalities on the space of continuous paths with respect to the uniform metric, for the law of the solution to a stochastic heat equation defined on $[0,T]\times {[0,1]}^d$. This equation is driven by the Gaussian ...

In this paper we first show a blow-up criterion for solutions to the Navier-Stokes equations with a time-independent force by using the profile decomposition method. Based on the orthogonal properties related to the profiles, we give some examples ...

We address the uniqueness of the nonzero stationary state for a reaction–diffusion system of Fisher–KPP type that does not satisfy the comparison principle. Although the uniqueness is false in general, it turns out to be true under biologically ...

This paper is concerned with a time-varying delayed hematopoiesis model with discontinuous harvesting terms. The harvesting terms considered in our hematopoiesis model are discontinuous which are totally different from the previous continuous, ...

In this paper, we analyze the existence and non-existence of nonnegative solutions to a class of nonlinear elliptic systems of type: $\{\begin{array}{rclll}-\mathrm{\Delta }u& =& {|\mathrm{\nabla }v|}^q+\lambda f& \text{in }& \mathrm{\Omega },\\ -\mathrm{\Delta }v& =& {|\mathrm{\nabla }u|}^p+\mu g& \text{in }& \mathrm{\Omega },\\ u=v& =& 0& \text{on }& \partial \mathrm{\Omega },\\ u,v& \ge & 0& \text{in }& \mathrm{\Omega },\end{array}$ where $\mathrm{\Omega }$ is a bounded domain of ${\mathbb{R}}^N$ and $p,q\ge 1$. $f,g$ are ...$\mathrm{}$

We study the Cauchy problem and the mixed initial boundary value problem of a fluid-particle interaction system in ${\mathbb{R}}^3$. A Serrin type criterion for the strong solution of the Cauchy problem is established in terms of ${\parallel \rho \parallel }_{L_t^{\mathrm{\infty }}{L}_x^{\mathrm{\infty }}}$ and ${\parallel u\parallel }_{L_t^s{L}_x^r}$, where $\mathrm{...}\mathrm{}\mathrm{}$$\mathrm{}\mathrm{}$

The purpose of this note is three-fold. First, a sharp threshold of global existence versus blow-up dichotomy of solutions to some non-linear fractional coupled Schrödinger equations is investigated. Second, using the potential-well method, the ...

In this paper, we present some new $Z$-eigenvalue inclusion theorem for tensors by categorizing the entries of tensors, and prove that these sets are more precise than existing results. On this basis, some lower and upper bounds for the $Z$-spectral ...$$

In data science, one is often confronted with a time series representing measurements of some quantity of interest. Usually, in a first step, features of the time series need to be extracted. These are numerical quantities that aim to succinctly ...

In this paper, we propose a line search penalty-free method for solving nonlinear second-order cone programming (NSOCP) problem. Compared with the traditional SQP-type method for NSOCP, our method does not need the assumption that the subproblem ...

We develop versions of the subgradient extragradient method for variational inequalities in Hilbert spaces and establish sufficient conditions for their convergence. First we prove a sufficient condition for a weak convergence of a recent existing ...$$

This paper uses Lie symmetry methods to analyze boundary crossing probabilities for a large class of diffusion processes. We show that if the Fokker–Planck–Kolmogorov equation has non-trivial Lie symmetry, then the boundary crossing identity ...

This paper is devoted to study the following equation $-\mathrm{\Delta }u+\lambda u={|u|}^{p-1}u\text{in}\mathrm{\Omega }$, with homogeneous Dirichlet or Neumann boundary conditions where $p>1$, $\lambda >0$, $\mathrm{\Omega }={\mathbb{R}}^{n-k}\times \omega$, $n\ge 2$, $k\ge 1$, and $\omega$ is a smoothly bounded domain of ${\mathbb{R}}^k$. We prove Liouville-type theorems for $C^{\mathrm{...}}$$\mathrm{}$${}_{}{}_{}$${}_{}$$$$\mathrm{}$$\mathrm{}$

We study symmetric properties of positive solutions to the Choquard type equation ${(-\mathrm{\Delta })}_p^{s}u+{|x|}^{a}u=(\frac{1}{{|x|}^{n-\alpha }}\ast u^q)u^r\text{in}{\mathbb{R}}^n,$ where $0<s<1$, $0<\alpha <n$, $p\ge 2$, $q>1$, $r>0$, $a\ge 0$ and ${(-\mathrm{\Delta })}_p^s$ is the fractional $p$-Laplacian. Via a direct method of moving planes, we prove ...$$$\mathrm{}$

We prove the existence of a fundamental solution of the Cauchy initial boundary value problem on the whole space for a parabolic partial differential equation with discontinuous unbounded first-order coefficient at the origin. We establish also ...

We present a new mathematical model for acid-mediated tumor invasion encompassing chemotherapy treatment. The model consists of a mixed ODE-PDE system with four differential equations, describing the spatio-temporal dynamics of normal cells, tumor ...

In this paper, we consider nonlinear wave equations with dissipation having the form $u_{tt}-\text{div}\left({|\mathrm{\nabla }u|}^{\gamma -2}\mathrm{\nabla }u\right)+b(t,x){|u_t|}^{m-2}{u}_t=g(x,u)$ for $(t,x)\in [0,\mathrm{\infty })\times {\mathbb{R}}^n$. We obtain existence and blow up results under suitable assumptions on the positive function $b(t,x)$ ...$$

In this paper, decay rates of the compressible Hall-MHD equations for quantum plasmas in three-dimensional whole space are studied. By using a general energy method, the time decay rates for higher-order spatial derivatives of density, velocity ...${\stackrel{}{}}^{}$$\mathrm{}\frac{\mathrm{}}{\mathrm{}}$

Let $Y$, $X$ and $\epsilon$ be continuous univariate random variables satisfying the model $Y=X+\epsilon$. Herein $X$ is of interest, $Y$ is a noisy version of $X$, and $\epsilon$ is a random noise independent of $X$. This paper is devoted to a nonparametric estimation of cumulative ...${}_{}$$$${}_{\mathrm{}}{}_{}$${}_{\mathrm{}}^{}{}_{}^{}$$$$$${}_{}$$$${}_{}$$$

In this paper, we consider minimal time problems governed by control-affine-systems in the plane, and we focus on the synthesis problem in presence of a singular locus that involves a saturation point for the singular control. After giving ...

The solutions of the Riemann problem for the isentropic relativistic Euler equations with the extended Chaplygin gas are constructed completely for all the possible cases. The asymptotic limits of solutions to the Riemann problem for the ...

We describe the dynamics of the 3-dimensional competitive Lotka–Volterra systems $\dot{x}=x(a-x-y-z),\dot{y}=y(b-x-y-z),\dot{z}=z(c-x-y-z),$ providing the phase portraits for all the values of the parameters $a$, $b$ and $c$ with $0<a<b<c$ in the positive octant of the ...

Let $p>0$ and ${(-\mathrm{\Delta })}^s$ is the fractional Laplacian with $0<s<1$. The purpose of this paper is to establish a classification result for positive stable solutions to a fractional singular elliptic equation with weight ${(-\mathrm{\Delta })}^{s}u=-h(x)u^{-p}\text{ in }{\mathbb{R}}^N.$ Here $N>2s$ and $h$ ...${}^{}$$\mathrm{}$$$$\mathrm{}\frac{\mathrm{}\mathrm{}}{\mathrm{}}\sqrt{{}^{\mathrm{}}}$${}_{}$${}_{}\begin{array}{cc}\frac{{\mathrm{}}^{\mathrm{}}\mathrm{}\mathrm{}\mathrm{}\sqrt{{\mathrm{}}^{\mathrm{}}\mathrm{}\mathrm{}}}{\mathrm{}\mathrm{}\mathrm{}}\hfill & \mathrm{}\mathrm{}\hfill \\ \mathrm{}\hfill & \mathrm{}\mathrm{}\hfill \end{array}$

In this paper, we present the construction and analysis of a fractional Zener model for modeling waves propagation in dissipative media, which leads to a more realistic mathematical model. We achieve its mathematical analysis: existence and ...

Given a countable set of families $\{{\mathcal{D}}_k:k\in \mathbb{N}\}$ of pseudometrics over the same set $D$, we study the power-aggregations of this class, that are defined as convex combinations of integral averages of powers of the elements of ${\cup }_k{\mathcal{D}}_k$. We prove that a ...$$${}_{}{\mathcal{}}_{}$$$$$${\mathcal{}}_{}$$$$$

Differentiation is one of the most common subjects of numerical calculations. Gradients and Hessians are used in many problems of the physical and engineering sciences. Automatic differentiation (AD) is usually employed when the accuracy in ...

We employ the viscosity solution technique to analyze optimal stopping problems with regime switching. To be specific, we show the viscosity property of value functions with the help of dynamic programming, and more importantly, provide a mild and ...