This study investigates the propagation of Stoneley waves at the interface between two semi-infinite, size-dependent couple stress solids, taking into account imperfect interface conditions and governed by Wiechert’s conditions. Traditional ...

In this paper, we consider the propagation of chaos on bounded convex domains. Under some suitable assumptions, the empirical measure of a large number of particles on a bounded domain is shown to approximate the solution of the porous medium ...

In this paper, a nonlocal reaction–diffusion–advection model with nonlinear boundary conditions arising from phytoplankton species is investigated, where the species depends solely on light for its metabolism. Firstly, we prove that a single ...

We show the lifespan of a strong solution to the incompressible 3D axially symmetric Euler system in ${\mathbb{R}}^3$ can be arbitrarily large if the initial swirl is small enough. A precise lower bound of the lifespan, depending on the size of $\Vert \mathrm{\nabla }\times (v_{0,\theta }{\mathit{e}}_{\mathit{\theta }}){\Vert }_{L^{\infty }}$, ...

We investigate the wave structure and new phenomena of the Riemann problems of isentropic compressible Euler equations with discontinuous flux in momentum caused by different equations of states, including pressureless flow and Chaplygin gas. ...

This work deals with a three-component chemotaxis system $$\begin{array}{c}\hfill \left\{\begin{array}{cc}{u}_t=\mathrm{\Delta }u-\mathrm{\nabla }·(u{\chi }_1(w)\mathrm{\nabla }w)+w-{\mu }_1{u}^2,\hfill & x\in \mathrm{\Omega },t>0,\hfill \\ v_t=\mathrm{\Delta }v-\mathrm{\nabla }·(v{\chi }_2(w)\mathrm{\nabla }w)+w+ruv-{\mu }_2{v}^2,\hfill & x\in \mathrm{\Omega },t>0,\hfill \\ w_t=\mathrm{\Delta }w+u+v-w,\hfill & x\in \mathrm{\Omega },t>0,\hfill \end{array}\right)\end{array}$$describing the spatiotemporal Alopecia Areata dynamics with signal-dependent sensitivity under ...$\mathrm{}{\mathbb{}}^{}\mathrm{}$${}_{\mathrm{}}$${}_{\mathrm{}}$${}_{}\mathrm{}\mathrm{}$

The solution of one-dimensional nonlinear problem of stationary heat conduction in a dielectric layer with volumetric energy release at a constant difference in electric potentials on the curvilinear heat transfer surfaces, bounding the layer, is ...

In this paper, we deal with the following quasilinear chemotaxis–consumption system with degenerate signal-dependent motility $$\begin{array}{c}\hfill \left\{\begin{array}{cc}{u}_t=\mathrm{\nabla }·(v^{\alpha }\mathrm{\nabla }{u}^m)+\alpha \mathrm{\nabla }·(v^{\alpha -1}u\mathrm{\nabla }v)+ru-\mu u^2,\hfill & x\in \mathrm{\Omega },t>0,\hfill \\ v_t=\mathrm{\Delta }v-uv,\hfill & x\in \mathrm{\Omega },t>0,\hfill \end{array}\right)\end{array}$$under the homogeneous Neumann boundary condition in $\mathrm{\Omega }\subset {\mathbb{R}}^n(n\ge 1)$ ...$\mathrm{}$$\mathrm{}$$$\begin{array}{c}\hfill {}_{{}^{}\mathrm{}}{}_{{}^{\mathrm{}}\mathrm{}}\end{array}$$$\mathrm{}$$\mathrm{}$$\mathrm{}$

In this study, we investigate the (3+1) q-deformed tanh-Gordon equation due to its importance in the context of mathematical physics. It describes solitonic solutions in quantum field theory; it can sometimes be used in condensed matter physics to ...$\frac{{\mathfrak{}}^{}}{{\mathfrak{}}^{}\mathfrak{}}$

The paper aims at studying dispersion of elastic waves in a sandwich plate with the parameters, characteristic of aerogel core and hard skin layers, typical for aerospace applications including optimal design of fuselage structural components. The ...

We present an asymptotic framework that rigorously generates nonlinear constitutive relations between stress and linearized strain for elastic bodies. Each of these relations arises as the leading-order relationship satisfied by a one-parameter ...

Coupled nonlocal nonlinear wave equations describe the dynamics of wave systems with multiple interacting components in a wide range of physical applications. Investigating the long-time behavior of the solutions is crucial for understanding the ...

This work is concerned with establishing the existence and uniqueness of the solution to a mixed-type degenerate boundary value problem for a relativistic magnetohydrodynamic system. We first consider a full relativistic magnetohydrodynamic system ...

The aim of this paper is to investigate the initial-boundary value problem of a possibly degenerate reaction-diffusion system over $\mathrm{\Omega }\subset {\mathbb{R}}^n$ with $n\ge 1$ of the following form $$\begin{array}{c}\hfill \left\{\begin{array}{cc}& {\partial }_t{m}_i-\kappa \mathrm{\Delta }{m}_i+{|m_i|}^{\gamma -2}{m}_i={({\partial }_{x_i}p)}^2,\hfill \\ \hfill & -\mathrm{\nabla }·[\mathbf{m}\mathrm{\nabla }p]=S,\hfill \end{array}\right)\end{array}$$with $\mathbf{m}=\text{diag}(m_1,\cdots ,m_n)$, the diffusivity $\kappa >0$,...$\mathrm{}$$\mathrm{}$$\mathrm{}$

It has been observed in experiments that, for some materials, when a sheet is subjected to increasing equal biaxial tensile forces on its edges, its deformation can change from homogeneous equal biaxial extension to homogeneous unequal biaxial ...

This paper is concerned with the traveling waves for a modified Holling-Tanner predator–prey model with degenerate diffusion. Different from the established approaches of constructing upper-lower solutions, we construct a new and suitable pair of ...${}^{}$$\mathrm{}$${}^{}\mathrm{}\sqrt{}$$\mathrm{}$

In this paper, we investigate singularity formation for the high-order generalized Fokas–Olver–Rosenau–Qiao equation which include the celebrated Fokas–Olver–Rosenau–Qiao equation (or also called the modified Camassa–Holm equation), and we are ...

This paper deals with the existence of forced waves for an epidemic model of West Nile virus in a shifting environment. Here a forced wave is a traveling wave with wave speed the same as the environmental shifting speed. The forced waves we ...

This paper involves a diffusive epidemic model whose domain has one free boundary with the Stefan boundary condition, and one fixed boundary subject to the usual homogeneous Dirichlet or Neumann condition. By using the standard upper and lower ...${\mathcal{}}_{\mathrm{}}$$\mathrm{}{}_{\mathrm{}}$${}_{\mathrm{}}$${}_{\mathrm{}}$${}_{\mathrm{}}{}_{\mathrm{}}$

We consider the CH–KP-I equation. For this equation, we prove the existence of steady solutions, which are solitary in one horizontal direction and periodic in the other. We show that such waves bifurcate from the line solitary wave solutions, ...