Zeitschrift für Angewandte Mathematik und Physik (ZAMP)

This focuses on the large time behavior of the solution to the IVP of the 2D fully dissipative magnetohydrodynamics system. We first compute the decay rates of the solutions, then, we show that these rates are sharp. Moreover, the explicit ...

We consider the inhomogeneous nonlinear Schrödinger equation with inverse-square potential in ${\mathbb{R}}^N$$$\begin{array}{c}\hfill i{u}_t-{\mathcal{L}}_{a}u+{\lambda |x|}^{-b}{|u|}^{\alpha }u=0,{\mathcal{L}}_a=-\mathrm{\Delta }+\frac{a}{{|x|}^2},\end{array}$$where $\lambda =\pm 1$, $\alpha ,b>0$ and $a>-\frac{{(N-2)}^2}{4}$. We first establish sufficient conditions for global existence and blow-up in $H_a^1({\mathbb{R}}^N)...$$\mathrm{}$${}_{}^{\mathrm{}}{\mathbb{}}^{}$${}^{\mathrm{}}$${}_{}^{\mathrm{}}{\mathbb{}}^{}$

The dynamics of biofilm lifecycle are deeply influenced by the surrounding environment and the interactions between sessile and planktonic phenotypes. Bacterial biofilms typically develop in three distinct stages: attachment of cells to a surface, ...

The main purpose of this research is to find new and more exact closed form solutions of an important integrable model in theoretical physics namely coupled Gerdjikov–Ivanov equation by utilizing the Lie symmetry approach. Lie group analysis has ...

We study a chemotaxis-Stokes system with signal consumption and logistic source terms of the form

We prove the existence and uniqueness of the solutions to a Caputo–Hadamard fractional stochastic differential equation driven by a multiplicative white noise, which may describe the random phenomena in the ultraslow diffusion processes. The ...

In a private communication with D. M. Barnett, W. D. Nix presented a series of numerical computations in which he calculated the net interaction force between two skew dislocations separated by a distance h that are parallel to the traction-free ...

We derive Papkovich–Neuber type representations for the solutions of Navier–Lamé equations in linear elastostatics and of the stationary Stokes equations using exterior calculus on the Euclidean space. We generalize the result for two-dimensional ...

Consider weak solutions u of the 3D Navier–Stokes equations in the critical space $$\begin{array}{c}\hfill u\in L^p\left(0,,,\infty ,;,{\dot{B}}_{q,\infty }^{\frac{2}{p}+\frac{3}{q}-1},({\mathbb{R}}^3)\right),2<p<\infty ,2\le q<\infty \mathrm{and}\frac{1}{p}+\frac{3}{q}\ge 1.\end{array}$$Firstly, we show that although the initial perturbations $w_0$ from u are large, every perturbed weak solution v ...$$${}_{\mathrm{}}$${}_{{}^{\mathrm{}}}$$\mathrm{}{\stackrel{}{}}_{}^{\frac{\mathrm{}}{}\mathrm{}}{\mathbb{}}^{\mathrm{}}$$\mathrm{}\mathrm{}$

In this paper, we study a Timoshenko system only with thermodiffusion effects. We establish exponential energy decay of the system with two kinds of boundary conditions under the assumption of the equal wave speeds. Our result extends the recent ...

Viscous flow through a reservoir with porous boundary is studied via asymptotic analysis and homogenization. Under the assumption of periodicity of the pores, the effective boundary condition is derived and rigorously justified. The velocity on ...

In this paper, we concerned with a haptotaxis system proposed as a model for fusogenic oncolytic virotherapy and syncytia, accounting for interaction between uninfected cancer cells, infected cancer cells, syncytia cancer cells, extracellular ...

In this paper, we deal with issues related to global multiplicity of $W_{\mathrm{loc}}^{1,p}(\mathrm{\Omega })$-solutions for the very-singular and non-local $\mu$-problem $$\begin{array}{c}\hfill -g\left(\underset{\mathrm{\Omega }}{\int },u^q\right){\mathrm{\Delta }}_{p}u=\mu u^{-\delta }+u^{\beta }\text{in}\mathrm{\Omega },u>0\text{in}\mathrm{\Omega }\text{and}u=0\text{on}\partial \mathrm{\Omega },\end{array}$$where $\mathrm{\Omega }\subset {\mathbb{R}}^N$ is a smooth bounded domain, $\delta >0$, $q>0$, $0<\beta \le p-1$ and $g:[0,\infty )\to [0,\infty )...$$\mathrm{}$$\mathrm{}{}_{\mathrm{}}$$\mathrm{}$${}_{\mathrm{}}$$\mathrm{}$$\mathrm{}$${}_{\mathrm{}}^{\mathrm{}}\mathrm{}$

The stabilization properties of dissipative Timoshenko systems have been attracted the attention and efforts of researchers over the years. In the past 20 years, the studies in this scenario distinguished primarily by the nature of the coupling ...

The paper is devoted to the study of the asymptotic speed of spread and traveling wave solutions for a time-periodic reaction–diffusion SI epidemic model which lacks the comparison principle. By using the basic reproduction number $R_0$ of the ...${}^{}$${}_{\mathrm{}}\mathrm{}$$$${}_{\mathrm{}}\mathrm{}$${}_{\mathrm{}}$${}^{}$

Based on the equations of the f-plane shallow water model, a new set of nonlinear models for the interaction of the vortices in the f-plane shallow water system are established by using perturbation expansion and multi-scale method. These models ...

The problem of axially symmetric TM wave diffraction from the finite, perfectly conducting bicone formed by a pair of finite cones of an arbitrary lengths and opening angles is considered. The problem is formulated in the spherical coordinate ...

We are concerned here with an analysis of the nonlinear irrotational gravity water wave problem with a free surface over a water flow bounded below by a flat bed. We employ a new formulation involving an expression (called flow force) which ...

In this paper, we establish transfer matrix for an incompressible orthotropic elastic layer. It is explicit and expressed compactly in terms of square brackets. This transfer matrix is a very convenient tool for solving various problems of wave ...

In this paper, we consider a new Timoshenko beam model with thermal and mass diffusion effects where heat and mass diffusion flux are governed by Cattaneo’s law. Necessary and sufficient conditions for exponential stability are provided in terms ...${}_{\mathrm{}}$$\mathrm{}\sqrt{}$

We consider the transmission problem of couple stress elasticity in a fixed domain ${\mathrm{\Omega }}_{-}$ juxtaposed with a thin layer ${\mathrm{\Omega }}_{+}^{\delta }$. Our aim is to model the effect of the thin layer ${\mathrm{\Omega }}_{+}^{\delta }$ on the fixed domain ${\mathrm{\Omega }}_{-}$ by an impedance boundary condition. For that we use ...${\mathrm{}}_{}$${\mathrm{}}_{}$

This paper is concerned with the asymptotic profiles of positive solutions for diffusive logistic equations. The aim is to study the sharp effect of nonlinear diffusion functions. Both the classical reaction–diffusion equation and nonlocal ...

In this article, the inverse scattering transform is considered for the Gerdjikov–Ivanov equation with zero and non-zero boundary conditions by a matrix Riemann–Hilbert (RH) method. The formula of the soliton solutions is established by Laurent ...

In this paper, a variable-coefficient symbolic computation approach is proposed to solve the multiple rogue wave solutions of nonlinear equation with variable coefficients. As an application, a ($2+1$)-dimensional variable-coefficient Kadomtsev–...

We present a complete classification of the central configurations of the 5-body problem in a plane having the following properties: three bodies, denoted by 1, 2, 3, are at the vertices of an isosceles triangle, and the other two bodies are ...

According to the formulation of the nonlinear problem of stationary heat conduction in a homogeneous ellipsoid, when the intensity of volume energy release increases with temperature, a variational form of a mathematical model of a thermal ...

Describing the emerging macro-scale behavior by accounting for the micro-scale phenomena calls for microstructure-informed continuum models accounting properly for the deformation mechanisms identifiable at the micro-scale. Classical continuum ...

A general reaction–diffusion equation with nonlinear advection term having neither monotonicity nor variational structure is considered. This work is concerned with traveling waves for this type of equations. By constructing an invariant region ...

We consider a damped plate model with rotational forces in a bounded domain. The plate is either clamped or hinged. The rotational forces and damping involve the spectral fractional Laplacian with powers $\theta$ in [0, 1] and $\delta$ in [0, 2], respectively. ...$$$$$\mathrm{}\mathrm{}\mathrm{}$$$$$$\mathrm{}\mathrm{}$$\mathrm{}\mathrm{}$$$$\mathrm{}\mathrm{}$$$$$${}^{\frac{\mathrm{}}{\mathrm{}}}$$$$\mathrm{}$

In this article, numerical schemes are proposed for approximating the solutions, possibly measure-valued with concentration (delta shocks), for a class of nonstrictly hyperbolic systems. These systems are known to model physical phenomena such as ...