Zeitschrift für Angewandte Mathematik und Physik (ZAMP)

Previous efforts at solving an asymptotic, plane stress, steady-state crack propagation problem for a linear elastic/perfectly plastic material, under the von Mises yield condition, have failed to produce solutions that satisfy all necessary ...

The 2D magnetohydrodynamics equations with horizontal dissipation and horizontal magnetic diffusion are considered. The classical solution in $H^k$$(k\ge 2)$ has been obtained; due to partial dissipation and strong nonlinearity, the global well-posedness ...${}^{\mathrm{}}$${}^{\mathrm{}}$

The deformation and displacement phenomena of liquid droplets from solid substrates are important in sub-surface processes such as enhanced oil recovery, chemical processing, and others, where the velocity of the continuous fluid is a key ...$\mathrm{}$$\mathrm{}$$\mathrm{}$

The general scaling underlying the asymptotic derivation of 2D theory for thin shells from the original equations of motion in 3D elasticity fails for cylindrical shells due to the cancellation of the leading-order terms in the geometric relations ...

This paper studies the propagation thresholds in a diffusive epidemic model with latency and vaccination. When the initial condition satisfies proper exponential decaying behavior, we present the spatial expansion feature of the infected. ...

In this paper, we present a general method, based on the techniques of analytic continuation and conformal mapping, for the analytic solution of Eshelby’s problem concerned with a two-dimensional inclusion of arbitrary shape in an infinite ...

In this paper, we linearise the recently introduced geometrically nonlinear constrained Cosserat-shell model. In the framework of the linear constrained Cosserat-shell model, we provide a comparison of our linear models with the classical linear ...

This paper is concerned with the existence and stability of traveling waves for doubly degenerate diffusion equations, where the spatial diffusion operator is of the form ${\partial }_x(|{\partial }_x{u}^m{|}^{p-2}{\partial }_x{u}^m)$ with $m>0$ and $p>1$. It is proved that, for the slow ...$\mathrm{}\mathrm{}$${}^{}$${}^{}$${}^{}$$\mathrm{}\mathrm{}\mathrm{}$${}^{\mathrm{}}$

This paper aims as the stability and large-time behavior of 3D incompressible magnetohydrodynamic (MHD) equations with fractional horizontal dissipation and magnetic diffusion. By using the energy methods, we obtain that if the initial data are ...${}^{\mathrm{}}{\mathbb{}}^{\mathrm{}}$${\mathrm{}}^{\frac{\mathrm{}}{\mathrm{}}}$${}^{\mathrm{}}{\mathbb{}}^{\mathrm{}}{}_{}^{\mathrm{}}{\mathbb{}}^{\mathrm{}}$

We consider the Cauchy problem of the incompressible Navier–Stokes system coupled with a nonlinear Fokker–Planck equation. An explicit approximate system on the manifold M is established and the local-in-time existence and uniqueness in Sobolev ...${}^{}{\mathbb{}}^{}{}^{}{\mathbb{}}^{}{}^{}$$\mathrm{}\mathrm{}\mathrm{}\mathrm{}\mathrm{}$${}^{}$${\stackrel{}{}}_{}^{\mathrm{}\frac{\mathrm{}}{}}{\mathbb{}}^{}{\stackrel{}{}}^{\mathrm{}}{\mathbb{}}^{}{}^{}\mathrm{}\frac{\mathrm{}}{\mathrm{}}$

We study the asymptotic evolution of a family of dynamic models of crawling locomotion, with the aim to introduce a well-posed characterization of a gait as a limit behaviour. The locomotors, which might have a discrete or continuous body, move on ...

This paper reconsiders the two-species cancer invasion haptotaxis model without cell proliferation $$\begin{array}{c}\hfill \left\{\begin{array}{c}{c}_{1t}=\mathrm{\Delta }{c}_1-{\chi }_1\mathrm{\nabla }·(c_1\mathrm{\nabla }v)-f(v)m{c}_1,\hfill \\ c_{2t}=\mathrm{\Delta }{c}_2-{\chi }_2\mathrm{\nabla }·(c_2\mathrm{\nabla }v)+f(v)m{c}_1,\hfill \\ \tau m_t=\mathrm{\Delta }m+c_1+c_2-m,\hfill \\ v_t=-mv+\eta v(1-{\alpha }_1{c}_1-{\alpha }_2{c}_2-v)\hfill \end{array}\right)(\star )\end{array}$$in a bounded and smooth domain $\mathrm{\Omega }\subset {\mathbb{R}}^2$ with homogeneous ...${}_{\mathrm{}}{}_{\mathrm{}}\mathrm{}$$\mathrm{}\mathrm{}$${}^{\mathrm{}}\left(,\mathrm{},,,,,,\mathrm{},,,\right)$$\mathrm{}\mathrm{}$${}_{\mathrm{}}{}_{\mathrm{}}\mathrm{}$$$$\mathrm{}$$$$$$\mathrm{}$${}_{\mathrm{}}{}_{\mathrm{}}\mathrm{}$$$$\mathrm{}\mathrm{}$$$

In this paper, we investigate the existence and uniqueness of $(\omega ,Q)$-periodic mild solutions for the following problem $$\begin{array}{c}\hfill x^{\prime }(t)=Ax(t)+f(t,x(t)),t\in \mathbb{R},\end{array}$$on a Banach space X. Here, A is a closed linear operator which generates an exponentially stable $C_0$-...$$

This paper investigates the global well-posedness and the stability of perturbations near a background magnetic field on the 2D incompressible anisotropic magnetohydrodynamic equations. More precisely, we consider the system with partial mixed ...${}^{\mathrm{}}$${\stackrel{}{}}^{}$

The $(3+1)$-dimensional [$(3+1)$-d] Mel’nikov equation describes an interaction between long-wave and short-wave packets in three-spatial dimensions, which is the coupling of $(3+1)$-d Kadomtsev–Petviashvili [KP] equation and nonlinear Schrödinger [NLS] ...$\mathcal{}\mathcal{}$$\mathrm{}\mathrm{}$$\mathrm{}\mathrm{}$$\mathrm{}\mathrm{}$

The higher-order modified Korteweg–de Vries (mKdV) equation with constants background is revealed based on the Riemann–Hilbert problem (RHP). With the derivation of RHP, the one-soliton solution (oSS) and simple breather solution (sBS) of the ...

The scattering of Love waves by an interface crack between a one-dimensional (1D) hexagonal quasicrystal (QC) coating and a half-space elastic substrate is investigated by using the superposition principle and integral transform technique. ...

The present paper is concerned with the existence of response solutions of quasi-periodic type for a class of quasi-periodically forced, non-Hamiltonian but reversible nonlinear beam equations. We do not suppose the basic frequency $\omega \in {\mathbb{R}}^2$ of the ...

This paper investigates a transmission problem of viscoelastic wave equations with degenerate nonlocal damping. We prove the global well-posedness of the problem with the aid of Faedo–Galerkin technique and the multiplier method. Meantime, by ...

Consider the following Schrödinger–Bopp–Podolsky system in ${\mathbb{R}}^3$ under an $L^2$-norm constraint, $$\begin{array}{c}\hfill \left\{\begin{array}{c}-\mathrm{\Delta }u+\omega u+\varphi u={u|u|}^{p-2},\hfill \\ -\mathrm{\Delta }\varphi +a^2{\mathrm{\Delta }}^2\varphi =4\pi u^2,\hfill \\ {\Vert u\Vert }_{L^2}=\rho ,\hfill \end{array}\right)\end{array}$$where $a,\rho >0$ are fixed, with our unknowns being $u,\varphi :{\mathbb{R}}^3\to \mathbb{R}$ and $\omega \in \mathbb{R}$. We prove that if $2<p<3$ (resp., $3<p<10/3$) and $\rho >0$ ...$\mathrm{}\mathrm{}\mathrm{}$$\mathrm{}$$\mathrm{}$${}^{\mathrm{}}$

We prove the global well-posedness for the 2D Boussinesq equations with a velocity damping term around the equilibrium state $(0,x_2)$ in the strip domain $\mathbb{R}\times (0,1)$ with Navier-type slip boundary condition. It is worth mentioning that the results of ...

In this paper, we give a new construction of $u_0\in B_{p,\infty }^{\sigma }$ such that the corresponding solution to the hyperbolic Keller-Segel model starting from $u_0$ is discontinuous at $t=0$ in the metric of $B_{p,\infty }^{\sigma }({\mathbb{R}}^d)$ with $d\ge 1$ and $1\le p\le \infty$, which implies the ill-posedness ...${}_{}^{}$$\mathrm{}$$\mathrm{}$

In this paper, the periodic traveling wave solution for a reaction–diffusion SIR epidemic model with demography and time-periodic coefficients is investigated. Because the traveling wave system of non-autonomous reaction–diffusion model is a ...${\mathcal{}}_{\mathrm{}}$${}^{}$${\mathcal{}}_{\mathrm{}}\mathrm{}$${}^{}$${}_{\mathrm{}}\mathrm{}$$\mathrm{}$

Pantographic structures attracted the attention of scientists thanks to their interesting mechanical behaviors. Since the 3D printing technology allows to produce polyamide (PA) and metallic (ME) samples, different kinds of experiments can be ...

Variation of the phase velocity, stress and displacement fields, and specific strain and kinetic energy in functionally graded (FG) rods with longitudinal exponential heterogeneity, are analyzed by a variant of Cauchy formalism, allowing ...

In this paper, we focus on the integrability of a generalized (2+1)-dimensional equation with three arbitrary constants. By using Bell polynomials, the Hirota bilinear form is derived, as well as the N-soliton solutions are solved. Then the ...

In this paper, we study a free boundary problem for a ratio-dependent predator–prey system in one space dimension, in which the free boundary is only caused by prey, representing the spreading fronts of prey. We discuss the long time behaviors of ...$$$$$$

In this paper, we investigate an inverse problem of recovering a space-dependent source in the generalized subdiffusion equation involving locally Lipschitz perturbations, where the additional observations take place at the terminal time and are ...

In this work, the solution regularity of a variable-order time-fractional diffusion equation with Mittag-Leffler kernel is analyzed and the uniqueness of determining the variable fractional order based on the observations of the solutions over a ...

We revisit the existence and stability of the critical front in the extended Fisher-KPP equation, refining earlier results of Rottschäfer and Wayne (J Differ Equ 176(2):532–560, 2001) which establish stability of fronts without identifying a ...