Zeitschrift für angewandte Mathematik und Physik

https://link.springer.com/journal/33

List of Papers (Total 228)

Multiscale modelling of fluid transport in vascular tumours subjected to electrophoresis anticancer therapies

Electrophoresis facilitated cancer treatment has demonstrated experimental efficacy in enhancing drug delivery within vascularised tumours. However, the lack of realistic mathematical models with direct measurements in the context of electrochemotherapy poses a challenge. We investigate the impact of an applied electric potential on the flow of Darcian-type fluid occurring in two...

A new example for the Lavrentiev phenomenon in nonlinear elasticity

We present a new example for the Lavrentiev phenomenon in context of nonlinear elasticity, caused by an interplay of the elastic energy’s resistance to infinite compression and the Ciarlet–Nečas condition, a constraint preventing global interpenetration of matter on sets of full measure.

Shear-induced wrinkling in accelerating thin elastic discs

The wrinkling instabilities produced by in-plane angular accelerations in a rotating disc are discussed here in a particular limit of relevance to very thin plates. By coupling the classical linear elasticity solution for this configuration with the Föppl–von Kármán plate buckling equation, a fourth-order boundary-value problem with variable coefficients is obtained. The singular...

Shooting for collinear periodic orbits in the Helium model

The frozen-planet periodic orbit of the classical collinear Helium model with negative energy is shown to exist by a simple shooting argument. This simplifies the approach established in Cieliebak et al. (Ann Inst H Poincaré Anal Non Linéaire 40:379–455, 2022). With this argument, it also follows that the algebraic count of the number of such orbits with a given negative energy...

A robust way to justify the derivative NLS approximation

The derivative nonlinear Schrödinger (DNLS) equation can be derived as an amplitude equation via multiple scaling perturbation analysis for the description of the slowly varying envelope of an underlying oscillating and traveling wave packet in dispersive wave systems. It appears in the degenerated situation when the cubic coefficient of the similarly derived NLS equation...

A short remark on inviscid limit of the stochastic Navier–Stokes equations

In this article, we study the inviscid limit of the stochastic incompressible Navier–Stokes equations in three-dimensional space. We prove that a subsequence of weak martingale solutions of the stochastic incompressible Navier–Stokes equations converges strongly to a weak martingale solution of the stochastic incompressible Euler equations in the periodic domain under the well...

Pointwise stabilization of Bresse systems

Bresse system over the interval (0, L) with pointwise dissipation at $$\xi \in (0,{L})$$ is analyzed. The exponential stability of the related semigroup is shown provided the dissipative points are of the form $$\xi \in \mathbb {Q}{L}$$ and $$\xi \ne \frac{n}{2m+1}L$$ , where $$n,m\in \mathbb {N}$$ and n, and $$2m+1$$ are co-prime.

Dynamical analysis of an age-space structured malaria epidemic model

In this paper, we will revisit the model studied in Lou and Zhao (J Math Biol 62:543–568, 2011), where the model takes the form of a nonlocal and time-delayed reaction–diffusion model arising from the fixed incubation period. We consider the infection age to be a continuous variable but without the limitation of the fixed incubation period, leading to an age-space structured...

Capillarity-driven Stokes flow: the one-phase problem as small viscosity limit

We consider the quasistationary Stokes flow that describes the motion of a two-dimensional fluid body under the influence of surface tension effects in an unbounded, infinite-bottom geometry. We reformulate the problem as a fully nonlinear parabolic evolution problem for the function that parameterizes the boundary of the fluid with the nonlinearities expressed in terms of...

The 3-wave resonant interaction model: spectra and instabilities of plane waves

The three wave resonant interaction model (3WRI) is a non-dispersive system with quadratic coupling between the components that finds application in many areas, including nonlinear optics, fluids and plasma physics. Using its integrability, and in particular its Lax Pair representation, we carry out the linear stability analysis of the plane wave solutions interacting under...

Interface potential in composites with general imperfect transmission conditions

The model analyzed in this paper has its origins in the description of composites made by a hosting medium containing a periodic array of inclusions coated by a thin layer consisting of sublayers of two different materials. This two-phase coating material is such that the external part has a low diffusivity in the orthogonal direction, while the internal one has high diffusivity...

Global-in-time well-posedness of the one-dimensional hydrodynamic Gross–Pitaevskii equations without vacuum

We establish global-in-time well-posedness of the one-dimensional hydrodynamic Gross–Pitaevskii equations in the absence of vacuum in $$(1 + H^s) \times H^{s-1}$$ with $$s \ge 1$$ . We achieve this by a reduction via the Madelung transform to the previous global-in-time well-posedness result for the Gross–Pitaevskii equation in Koch and Liao (Adv Math 377, 2021; Adv Math 420...

A MGT thermoelastic problem with two relaxation parameters

In this paper, we consider, from both analytical and numerical viewpoints, a thermoelastic problem. The so-called MGT model, with two different relaxation parameters, is used for both the displacements and the thermal displacement, leading to a linear coupled system made by two third-order in time partial differential equations. Then, using the theory of linear semi-groups the...

The compressible Navier–Stokes equations with slip boundary conditions of friction type

We study a mathematical model of a viscous compressible fluid obeying the slip boundary condition of friction type. We present a notion of weak solutions to this model, in which the momentum equation and the associated energy inequality are combined into a single relation. Moreover, the slip boundary condition of friction type is incorporated into this relation by the use of a...

Asymmetric equilibrium configurations of a body immersed in a 2d laminar flow

We study the equilibrium configurations of a possibly asymmetric fluid–structure interaction problem. The fluid is confined in a bounded planar channel and is governed by the stationary Navier–Stokes equations with laminar inflow and outflow. A body is immersed in the channel and is subject to both the lift force from the fluid and to some external elastic force. Asymmetry, which...

Dynamical analysis for a diffusive SVEIR epidemic model with nonlinear incidences

In this article, we are concerned with a diffusive SVEIR epidemic model with nonlinear incidences. We first obtain the well-posedness of solutions for the model. Then, the basic reproduction number $$R_{0}$$ and the local basic reproduction number $${\overline{R}}_{0}(x)$$ are calculated, which are defined as the spectral radii of the next-generation operators. The relationship...

Curiosities of two-dimensional planing

The traditional deep-water analysis of two-dimensional planing is studied in detail and applied to efficient splash-free and optimal profiles, as well as to flat plates. The methodology is used to analyze both free-to-rise and free-to-rise-plus-trim profiles. In some cases, the predictions exhibit unexpected discontinuous behavior for the lift, wetted length and other results...

Global continua of solutions to the Lugiato–Lefever model for frequency combs obtained by two-mode pumping

We consider Kerr frequency combs in a dual-pumped microresonator as time-periodic and spatially $$2\pi $$ -periodic traveling wave solutions of a variant of the Lugiato–Lefever equation, which is a damped, detuned and driven nonlinear Schrödinger equation given by $$\textrm{i}a_\tau =(\zeta -\textrm{i})a-d a_{x x}-|a|^2a+\textrm{i}f_0+\textrm{i}f_1\textrm{e}^{\textrm{i}(k_1 x-\nu...

Critical velocities of a two-layer composite tube incorporating the effects of transverse shear, rotary inertia and material anisotropy

Critical velocities of a two-layer composite tube subjected to a uniform internal pressure moving at a constant velocity are analytically derived by using a first-order shear deformation shell theory incorporating the transverse shear, rotary inertia and material anisotropy. The composite tube consists of two perfectly bonded axisymmetric circular cylindrical layers of dissimilar...

Curved channels with constant cross sections may support trapped surface waves

Curved channels with constant cross sections are constructed which support a trapped surface wave. Since corresponding eigenvalues are embedded in the continuous spectrum of the water wave problem and therefore possess the natural instability, the construction procedure requires “fine-tuning” of several parameters in the (small) curvature of the channel as well as geometrical...

Multiplication of distributions in a linear gain and loss system

We consider a model of coupled oscillators which can be seen as a gain and loss system. In the attempt to quantize the system, we propose a new definition of multiplication between distributions, and we check that this definition can be adopted when checking the biorthonormality of the eigenstates of the Hamiltonian H of the system, and of its adjoint $$H^\dagger $$ . In the...

Wellposedness and regularity for linear Maxwell equations with surface current

We study linear time-dependent Maxwell equations on a cuboid consisting of two homogeneous subcuboids. At the interface, we allow for nonzero surface charge density and surface current. This model is a first step towards a detailed mathematical analysis of the interaction of single-layer materials with electromagnetic fields. The main results of this paper provide several...

Spatial dynamics of a viral infection model with immune response and nonlinear incidence

Incorporating humoral immunity, cell-to-cell transmission and degenerated diffusion into a virus infection model, we investigate a viral dynamics model in heterogenous environments. The model is assumed that the uninfected and infected cells do not diffuse and the virus and B cells have diffusion. Firstly, the well-posedness of the model is discussed. And then, we calculated the...

Combining effects ensuring boundedness in an attraction–repulsion chemotaxis model with production and consumption

This paper is framed in a series of studies on attraction–repulsion chemotaxis models combining different effects: nonlinear diffusion and sensitivities and logistic sources, for the dynamics of the cell density, and consumption and/or production impacts, for those of the chemicals. In particular, herein we focus on the situation where the signal responsible of gathering...

Dynamics of a diffusion epidemic SIRI system in heterogeneous environment

This paper studies the dynamical behaviors of a diffusion epidemic SIRI system with distinct dispersal rates. The overall solution of the system is derived by using $$L^{p}$$ theory and the Young’s inequality. The uniformly boundedness of the solution is obtained for the system. The asymptotic smoothness of the semi-flow and the existence of the global attractor are discussed...