Zeitschrift für Angewandte Mathematik und Physik (ZAMP)

We consider the following Kirchhoff equation in the Sobolev critical case with combined power nonlinearities

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We consider the linear elasticity system for a body coated with a thin elastic layer. The effect of the thin layer on that body can be described through an impedance operator linking the displacement and the traction on the interface. This ...

The aim of the present study is to design a solid material with specific and tailored mechanical properties through a suitably defined design framework and to evaluate the effectiveness of different microstructure geometries in an engineering ...

In this paper, we deal with a class of planar Schrödinger–Poisson systems, namely, $-\mathrm{\Delta }u+V(x)u+\frac{\gamma }{2\pi }(log(|·{|)\ast |u|}^2)u=b{|u|}^{p-2}u\text{in}{\mathbb{R}}^2$, where $\gamma >0$, $b\ge 0$, $p>2$ and $V\in C({\mathbb{R}}^2,\mathbb{R})$ is an unbounded potential function with ${inf}_{{\mathbb{R}}^2}V>0$. Suppose moreover that the potential ...$\left|,,,{\mathbb{}}^{\mathrm{}},,,,,,,\right|$$\mathrm{}$$\mathrm{}$$\mathrm{}$

We consider a nonlinear, hyperbolic population balance equation that incorporates both aggregation and collisional breakage events simultaneously. Our approach revolves around the development of a novel time-explicit finite volume scheme. Under a ...

This work is dedicated to the study of existence of solutions for a Schrödinger–Poisson type system involving possible different integrodifferential operators in the presence of a nonnegative but not bounded away from zero potential. We consider a ...${}^{\mathrm{}}$$\mathrm{}\mathrm{}\mathrm{}\mathrm{}$$$$$

In this paper, we consider a diffusive–advective predator–prey system in a spatially heterogeneous environment subject to a hostile boundary condition, where the interaction term is governed by a Holling type II functional response. We investigate ...

In this paper, we investigate the Cauchy problem of Keller–Segel–Navier–Stokes system with fractional diffusion. Making use of Fourier localization technique and Littlewood-Paley theory, we establish the global well-posedness of mild solution for ...

In this paper, we obtain the existence of a positive solution for a class of nonvariational fractional elliptic system with concave and convex nonlinearities in two cases. The paper is divided in two parts: In the first one, for general ...

This paper focuses on studying blow-up prevention by sub-logistic sources in 2D Keller–Segel chemotaxis systems with superlinear signal production. An application of a result on parabolic gradient regularity for parabolic equations in Orlicz ...

This paper studies an impact of media epidemic system with diffusion and linear source. We first derive the uniform bounds of solutions to impact on media reaction diffusion system. Then, the basic reproduction number is calculated and the ...$$

A nonlocal diffusion single population model with advection and free boundaries is considered. Our aim is to discuss how the advection rate affects dynamic behaviors of species under the case of small advection. Firstly, the well-posed global ...

We analyze the spectral and dynamical stability of solitary wave solutions to the Lugiato–Lefever equation on $\mathbb{R}$. Our interest lies in solutions that arise through bifurcations from the phase-shifted bright soliton of the nonlinear Schrödinger ...$\mathrm{}$$\mathrm{}$

In this article, a class of Caputo–Hadamard fractional stochastic differential equation (FSDEs) with time-delays and impulses is considered. With the help of contraction mapping principle, we derive the existence and uniqueness of the solutions to ...$\stackrel{}{}$

The current work investigates the transverse vibration of a piezothermoelastic (PTE) nanobeam in the frame of dual-phase-lag thermoelasticity theory. Closed-form analytical expression for the thermoelastic damping (TED) in terms of quality factor ...

This study investigates the thermocapillary migration of a compound drop placed concentrically within a spherical cavity under the limit of vanishing Péclet and Reynolds number. The imposed temperature gradient, which is constant along the line ...

A recent theoretical study (Xu in Proc R Soc A Math Phys Eng Sci 477:20200913, 2021) has derived conditions on the coefficients of Jeffreys-type equation to predict thermal oscillations and resonance during phonon hydrodynamics in non-metallic ...$\mathrm{}\mathrm{}$

How to free a road from vehicle traffic as efficiently as possible and in a given time, in order to allow for example the passage of emergency vehicles? We are interested in this question which we reformulate as an optimal control problem. We ...

In this paper, we study the Cauchy problem for a system of nonlinear Schrödinger equations with quadratic interactions and initial data belonging to a class of analytic Gevrey functions. Here, we present a local well-posedness result in the ...${}^{}{}^{}$$\mathrm{}$$$${}^{\mathrm{}}$$\mathrm{}\mathrm{}\mathrm{}$${}^{\mathrm{}}$$\mathrm{}\mathrm{}$

In this paper, we study the $\mathrm{\Gamma }$-limit of a properly rescaled family of energies, defined on a narrow strip, as the width of the strip tends to zero. The limit energy is one-dimensional and is able to capture (and penalize) concentrations of the ...$\mathrm{}$

In a recent paper Li et al. (Z Angew Math Phys 73:52, 2022. https://doi.org/10.1007/s00033-022-01681-4) have considered a generalized nonlinear Schrödinger equation which has extensive applications in various fields of physics and engineering. ...$\mathrm{}\mathrm{}$${}_{}$${}_{\mathrm{}}\left(,,\right)$

In this paper, we study multi-bump solutions of the following Kirchhoff type equation: $$\begin{array}{c}\hfill -M\left(,,\underset{{\mathbb{R}}^2}{\int },{|\mathrm{\nabla }u|}^2,\text{d},x\right)\mathrm{\Delta }u+\left(\mu ,V,(,x,),+,h,(,x,)\right)u=\lambda f(u)\text{in}{\mathbb{R}}^2,\end{array}$$where M is continuous with ${inf}_{{\mathbb{R}}^{+}}M>0$, $V\ge 0$ and its zero set has several disjoint bounded components, $\mu$, $\lambda$ are positive ...

This study developed a novel nonlocal numerical model based on the peridynamic differential operator to analyze the thermoelectric coupling field. The thermoelectric coupling equations and boundary conditions are transformed from the classical ...

In this paper, we study the possible singular points of suitable weak solutions to the 3D co-rotational Beris-Edwards system. Inspired by the work of He et al. (J. Nonlinear Sci. 29:2681–2698, 2019) and Wang et al. (Nonlinearity 32:4817–4833, 2019)...$\frac{\mathrm{}}{\mathrm{}}\mathrm{}$

The aim of this paper is to establish an Ambrosetti–Prodi type result involving Dirac weights $$\begin{array}{c}\hfill \left\{\begin{array}{cc}{u}^{\prime \prime \prime \prime }(x)+q(x)u(x)=(c(x)+\sum _{i=1}^p{c}_i\delta (x-x_i))(g(u(x))+f(x)),\hfill & x\in (0,1),\hfill \\ u(0)=u(1)=u^{\prime \prime }(0)=u^{\prime \prime }(1)=0,\hfill \end{array}\right)\end{array}$$where $\delta (x-x_i)$ is the canonical Dirac delta function at the point ${\mathrm{...}}_{}$$\mathrm{}\mathrm{}$$\mathbb{}$$\mathrm{}{}_{\mathrm{}}{}_{\mathrm{}}{}_{}{}_{\mathrm{}}\mathrm{}$$\mathrm{}\mathrm{}\mathrm{}$${}^{\mathrm{}}\mathrm{}\mathrm{}\mathbb{}$${}^{\mathrm{}}\mathbb{}\mathbb{}$$\mathrm{}\mathrm{}\mathrm{}$${}_{}\mathrm{}$

The main objective of this paper is to consider a continuous data assimilation algorithm for the three-dimensional planetary geostrophic model in the case that the observable measurements, obtained continuously in time, may be contaminated by ...

In this paper, we study the asymptotic behavior of transmission system for coupled Kirchhoff plates, where one equation is conserved and the other has dissipative property, and the dissipation mechanism is given by fractional damping ${(-\mathrm{\Delta })}^{2\theta }{v}_t$ with ...$\frac{\mathrm{}}{\mathrm{}}\mathrm{}$$\frac{\mathrm{}}{\mathrm{}}\frac{\mathrm{}}{\mathrm{}}$${}^{\mathrm{}\mathrm{}\mathrm{}}$$\frac{\mathrm{}}{\mathrm{}}\mathrm{}$${}^{\mathrm{}\mathrm{}\mathrm{}}$${}^{\mathrm{}\mathrm{}\mathrm{}}$$\mathrm{}$

The long-term behavior of low regularity solutions to the damped BBM equation with a distribution force on the torus is studied. Since the energy equation fails to hold for the low regularity solutions, the existence of a bounded absorbing set is ...