Zeitschrift für Angewandte Mathematik und Physik (ZAMP)

In this study, we start from a Follow-the-Leaders model for traffic flow that is based on a weighted harmonic mean (in Lagrangian coordinates) of the downstream car density. This results in a nonlocal Lagrangian partial differential equation (PDE) ...${}^{\mathrm{}}$

This paper is devoted to a mathematical model with diffusion and cross-diffusion to describe the interaction between vegetation and soil water. First, the existence of Hopf bifurcation and cross-diffusion-driven Turing instability are discussed. ...

In this paper, the full information about the existence and nonexistence of a time-periodic traveling wave solution of a reaction–diffusion Zika epidemic model with seasonality, which is non-monotonic, is investigated. More precisely, if the basic ...${}_{\mathrm{}}$${}^{}\mathrm{}$${}^{}$${}^{}$${}_{\mathrm{}}\mathrm{}$

A novel method is presented for explicitly solving inhomogeneous initial-boundary-value problems (IBVPs) on the half-line for a well-known coupled system of evolution partial differential equations. The so-called double-diffusion model, which is ...$$$$

The thermodynamic model of viscoelastic deformable solids at finite strains is formulated in a fully Eulerian way in rates. Also, effects of thermal expansion or buoyancy due to evolving mass density in a gravity field are covered. The Kelvin–...

The heat equation, based on Fourier’s law, is commonly used for description of heat conduction. However, Fourier’s law is valid under the assumption of local thermodynamic equilibrium, which is violated in very small dimensions and short ...

Considered herein is the well-posedness, asymptotic stability and blow-up of the initial-boundary value problem for nonlocal singular viscoelastic wave equation with logarithmic nonlinearity $u_{\mathit{tt}}-\frac{1}{x}{(x{u}_x)}_x-\frac{1}{x}{(x{u}_{\mathit{xt}})}_x+\underset{0}{\overset{t}{\int }}m(t-\lambda )\frac{1}{x}{(x{u}_x(x,\lambda ))}_x\text{d}\lambda ={|u|}^{r-2}u...$

We address the Prandtl equations and a physically meaningful extension known as hyperbolic Prandtl equations. For the extension, we show that the linearised model around a non-monotonic shear flow is ill-posed in any Sobolev spaces. Indeed, ...$\sqrt[\mathrm{}]{}$$\sqrt{}$$\mathrm{}$$\mathrm{}$$\sqrt{}$$\sqrt{}\sqrt{}$

A significant proportion of malaria infections in humans exhibit no symptoms, but it is a reservoir for maintaining malaria transmission. A time periodic reaction-diffusion model for malaria spread is introduced in this paper, incorporating ...${\mathcal{}}_{\mathrm{}}$${\mathcal{}}_{\mathrm{}}\mathrm{}$${\mathcal{}}_{\mathrm{}}\mathrm{}$${\mathcal{}}_{\mathrm{}}\mathrm{}$

The time-dependent electrophoresis of an infinitely cylindrical particle in an electrolyte solution, saturated in a charged porous medium after the sudden application of a transverse or tangential step electric field, is investigated semi-...

This paper is devoted to study the population dynamics of a single species in a one-dimensional environment which is modeled by a reaction–diffusion–advection equation with free boundary condition. We find three critical values $c_0$, 2 and ${\beta }^{\ast }$ for ...$$${}^{}\mathrm{}{}_{\mathrm{}}\mathrm{}$$\mathrm{}{}_{\mathrm{}}$${}_{\mathrm{}}\mathrm{}$$\mathrm{}{}^{}$${}^{}$$\mathrm{}$

Image inpainting is the process of restoring damaged areas in an image using information available from neighboring regions. In this paper, we present a novel, efficient, and simple local image inpainting algorithm based on the Allen–Cahn (AC) ...

We study an initial-boundary value problem of two-dimensional nonhomogeneous asymmetric fluids with magnetic field and density-dependent viscosity $\mu (\rho )$. Applying Desjardins’ interpolation inequality and delicate energy estimates, we show the ...$\mathrm{}{}_{\mathrm{}}{}_{{}^{}}$${}^{\mathrm{}}$

The direct and two inverse problems defined for an integro-differential equation on a bounded domain have been considered. The spectral problem of the integro-differential equation constitutes the Legendre differential equation in space variable. ...

The nonlocal residual symmetries of a generalized Broer–Kaup–Kupershmidt system are constructed using the truncated Painlevé expansion. By considering appropriate potential variables, these nonlocal symmetries are localized into Lie point ...

In this paper, we investigate the following nonlinear Choquard equation with prescribed $L^2$-norm constraint $$\begin{array}{c}\hfill \left\{\begin{array}{cc}-\mathrm{\Delta }u=\lambda u+(|x{|}^{-1}\ast |u{|}^2)u\hfill & \text{in}\mathrm{\Omega },\hfill \\ u=0\hfill & \text{on}\partial \mathrm{\Omega },\hfill \\ \underset{\mathrm{\Omega }}{\int }{|u|}^2\text{d}x=a^2,\hfill \end{array}\right)\end{array}$$where $a>0$, $\lambda \in \mathbb{R}$ appears as an unknown Lagrange multiplier and $\mathrm{\Omega }\subset {\mathbb{R}}^3$ is an exterior domain with ...$\mathrm{}\mathrm{}$${\mathbb{}}^{\mathrm{}}\mathrm{}$$\mathrm{}$${\mathbb{}}^{\mathrm{}}\mathrm{}$$\mathrm{}$$\mathrm{}$$\mathrm{}$

Starting from a mesoscopic description of cell migration and intraspecific interactions, we obtain by upscaling an effective reaction–diffusion–taxis equation for the cell population density involving spatial nonlocalities in the source term and ...

In this paper, a class of models with deep physical meaning is studied through duality, and positive Lyapunov exponents and some spectral properties are obtained under certain conditions.

The paper examines stochastic diffusion within an expanding space–time framework motivated by cosmological applications. Contrary to other results in the literature, for the considered general stochastic model, the expansion of space–time leads to ...

This article explores the Hilfer fractional derivative within the context of fractional differential equations and investigates a mathematical model formulated as a three-point boundary value problem (BVP). The primary focus is on the application ...$\mathrm{}$$\mathrm{}$

In this paper, a novel analytical approach based on nonlocal strain gradient theory is proposed to investigate small-scale effects on the radial vibration of isotropic spherical nanoparticles interacting with a viscoelastic fluid. The viscoelastic ...

The Yajima–Oikawa (YO) system is an important long-wave–short-wave resonant interaction model, which can be used to describe a fascinating resonance phenomena in diverse areas, such as hydrodynamics, nonlinear optics and biophysics. In this paper, ...

To solve fractional partial differential equations (FPDEs) under various physical conditions, this study developed a novel method known as the Hermite wavelet method employing the functional integration matrix. The method that has been suggested ...$\mathrm{}\mathrm{}$

This paper proposes, for particle-based materials, a higher-order nonlocal elasticity continuum model that includes the Piola peridynamics and the Eringen nonlocal elasticity. When referring to particle-based materials, we denote systems that can ...

In this paper, we consider the following quasilinear three-species predator–prey model with competition mechanism $$\begin{array}{c}\hfill \left\{\begin{array}{c}{u}_t=\mathrm{\nabla }·\left({\varphi }_1,\left(u\right),\mathrm{\nabla },u\right)-\mathrm{\nabla }·\left(u,{\psi }_1,\left(u\right),\mathrm{\nabla },w\right)+{\gamma }_{1}uw-{\theta }_{1}u-{\mu }_{1}uv,\hfill \\ v_t=\mathrm{\nabla }·\left({\varphi }_2,\left(v\right),\mathrm{\nabla },v\right)-\mathrm{\nabla }·\left(v,{\psi }_2,\left(v\right),\mathrm{\nabla },w\right)+{\gamma }_{2}vw-{\theta }_{2}v-{\mu }_{2}uv,\hfill \\ w_t=D\mathrm{\Delta }w-\left(u,+,v\right)w+\sigma w\left(1,-,w\right),\hfill \end{array}\right)\end{array}$$in a bounded smooth domain $\mathrm{\Omega }\subset {\mathbb{R}}^n\left(n,\ge ,2\right)$. The ...${}_{}{}_{}\mathrm{}$${}_{}\mathrm{}$$\mathrm{}\mathrm{}$${}_{}\left(\right)$${}_{}\left(\right)$$$\begin{array}{c}\hfill {}_{}\left(\right){}_{}{\left(,,\mathrm{}\right)}^{{}_{}}{}_{}\left(\mathrm{}\right)\mathrm{}{}_{}\left(\right){}_{}{\left(,,\mathrm{}\right)}^{{}_{}\mathrm{}}\end{array}$$$\mathrm{}$${}_{}\mathrm{}{}_{}\mathrm{}{}_{}{}_{}\mathbb{}\left(,,\mathrm{},,\mathrm{}\right)$$$\begin{array}{c}\hfill {}_{}\left\{{}_{},,\frac{\mathrm{}}{},,,\frac{\mathrm{}}{}\right\}\left(,,\mathrm{},,\mathrm{}\right)\end{array}$$${}_{}\mathrm{}{}_{}\mathrm{}\left(,,\mathrm{},,\mathrm{}\right)$

We are concerned with the isentropic compressible Navier–Stokes system in the two-dimensional torus, with rough data and vacuum; the initial velocity belongs to the Sobolev space $H^1$ and the initial density is only bounded and nonnegative. ...

Assuming that the streamlines are given by keeping constant one of the two orthogonal curvilinear coordinates in the Euclidean two-dimensional space, while considering a steady, two-dimensional, isentropic flow of an ideal gas through a convergent-...

In this paper, we study the following biharmonic Choquard-type problem $$\begin{array}{c}\hfill \begin{array}{c}\hfill \left\{\begin{array}{c}{\mathrm{\Delta }}^{2}u-\beta \mathrm{\Delta }u=\lambda u+(I_{\mu }\ast F(u))f(u),\text{in}{\mathbb{R}}^4,\hfill \\ {\displaystyle \underset{{\mathbb{R}}^4}{\int }{|u|}^2\text{d}x=c^2>0,u\in H^2({\mathbb{R}}^4),}\hfill \end{array}\right)\end{array}\end{array}$$where $\beta \ge 0$, $\lambda \in \mathbb{R}$, $I_{\mu }=\frac{1}{{|x|}^{\mu }}$ with $\mu \in (0,4)$, F(u) is the primitive function of f(u), and f is a continuous function with ...

In this article, we study a class of differential quasi-variational–hemivariational inequalities involving time delays. We establish new systems and prove the solvability and the existence of decay solutions. Moreover, we are concerned with long-...

In this article, we consider the optimal control problem governed by the wave equation in a 2-dimensional domain ${\mathrm{\Omega }}_{ϵ}$ in which the state equation and the cost functional involves highly oscillating periodic coefficients $A^{ϵ}$ and $B^{ϵ}$, respectively. This ...