Zeitschrift für angewandte Mathematik und Physik最新文献

In this paper, we study the following two-species chemotaxis system with generalized volume-filling effect and general kinetic functions

under homogeneous Neumann boundary conditions in a smoothly bounded domain (Omega subset {mathbb {R}}^{n}) ((nge 1)), where (a_{1}, a_{2}, mu _{1}, mu _{2}) are positive constants. When the functions (D_{i}, S_{i}, f_{i}, g_{i}) ((i=1,2)) belong to (C^{2}) fulfilling some suitable hypotheses, we study the global existence and boundedness of classical solutions for the above system and find that under the case of (tau =1) or (tau =0), either the higher-order nonlinear diffusion or strong logistic damping can prevent blow-up of classical solutions for the problem. In addition, when the functions are replaced to Lotka–Volterra competitive kinetic functional response term and linear signal generations, by constructing some appropriate Lyapunov functionals, we show that the solution convergences to the constant steady state in (L^{infty }(Omega )) in the case of (a_1, a_2 in (0,1)) or (a_1 ge 1>a_2 > 0) under some more concise conditions than [2], which improved the existing conditions to some extent.

In this paper, we pursue our series of papers aiming to show the applicability of the concept of very weak solutions. We consider a wave model with irregular position-dependent mass and dissipation terms, in particular, allowing for (delta )-like coefficients and prove that the problem has a very weak solution. Furthermore, we prove the uniqueness in an appropriate sense and the coherence of the very weak solution concept with classical theory. A special case of the model considered here is the so-called telegraph equation.

In this paper, we consider the following nonlinear Choquard equation with magnetic field

where (varepsilon >0) is a small parameter, (Nge 3), (0<mu <N), (2_{mu }^{*}=frac{2N-mu }{N-2}), (V(x):{mathbb {R}}^{N}rightarrow {mathbb {R}}^{N}) and (A(x):{mathbb {R}}^{N}rightarrow {mathbb {R}}^{N}) is a continuous potential, f is a continuous subcritical term, and F is the primitive function of f. Under a local assumption on the potential V, by the variational methods, the penalization techniques and the Ljusternik–Schnirelmann theory, we prove the multiplicity and concentration properties of nontrivial solutions of the above problem for (varepsilon >0) small enough.

This paper deals with a parabolic–elliptic Keller–Segel chemotaxis-growth system with flux limitation

under homogeneous Neumann boundary conditions, where (Omega subset {mathbb {R}}^N) is a smoothly bounded domain, (min {mathbb {R}}), (lambda>0, mu >0), (k>1), (M(t):=frac{1}{|Omega |} mathop {int }limits _{Omega } u(x, t) d x), (fleft( |nabla v|^2right) =(1+|nabla v|^2)^{-alpha }, alpha in {mathbb {R}}). In this framework, it is shown that when (Nge 2, m+k>2, k>1, kge m) and

then for all nonnegative initial data, the solution is global and bounded in time. Moreover, when (Omega subset {mathbb {R}}^N) ((Nge 5)) is a ball, if (1<m<min left{ frac{2N-4}{N},1-frac{1}{N}+frac{1}{N}sqrt{N^2-4N+1}right} ) and the parameters (alpha ) and k satisfy suitable conditions, there exist some initial data (u_{0}) such that the solution u(x, t) blows up at finite time (T_{max }) in (L^{infty })-norm sense.

This paper deals with a chemotaxis-Navier–Stokes model with indirect signal production involving Dirichlet signal boundary condition in a bounded domain with smooth boundary. A recent literature has asserted that for all reasonably regular initial data, the associated no-flux/saturation/no-flux/no-slip problem possesses at least one globally defined weak solution in the logistic-type degradation here is weaker than quadratic case. But the knowledge on regularity properties of solution has not yet exceeded some information on fairly basic integrability features. The present study reveals that each of these weak solutions becomes eventually classical and bounded under some suitably strong sub-quadratic degradation assumption and an explicit smallness condition. Furthermore, in comparison with the related contributions in the case of the direct signal production, our findings inter alia rigorously reveal that the indirect signal production mechanism genuinely contributes to the global solvability and eventual smoothness of the chemotaxis-Navier–Stokes system.

In this paper, we consider an initial and boundary value problem to the three-dimensional (3D) nonhomogeneous nematic liquid crystal flows with density-dependent viscosity and vacuum. Combining delicate energy method with the structure of the system under consideration, the global well-posedness of strong solutions is established, provided that (Vert rho _{0}Vert _{L^{1}}+Vert nabla varvec{d}_0Vert _{L^2}) is suitably small. In particular, the initial velocity can be arbitrarily large. Moreover, the exponential decay rates of the strong solution are also obtained.

This paper deals with an initial-boundary value problem in two-dimensional smoothly bounded domains for the system

which describes the mutual interaction of chemotactically moving microorganisms and their surrounding incompressible fluid, where (kappa in mathbb {R}), the gravitational potential (phi in W^{2,infty }(Omega )), and (mathcal {S}(n)) satisfies

Under the boundary conditions

it is shown in this paper that suitable regularity assumptions on the initial data entail the following: (i) If (alpha >-1) and (kappa =0), then the simplified chemotaxis-Stokes system possesses a unique global classical solution which is bounded. (ii) If (alpha ge 0) and (kappa in mathbb {R}), then the full chemotaxis-Navier–Stokes system admits a unique global classical solution.

It is known that an incident bulk P wave propagating in a homogeneous isotropic halfspace, being reflected from the plane boundary, may exhibit a mode conversion into shear S wave without the formation of reflected P waves. The mode conversion takes place, when the incident wave hits the boundary at some critical angles, which depend upon Poisson’s ratio. Herein, it is revealed that the Jeffreys solution for the mode conversion angles needs in in corrections, mainly because of spurious roots, appeared at solving a specially constructed eighth-order polynomial for the P wave reflection coefficient. The developed approach allowed us to construct a bi-cubic polynomial and obtain analytical expressions for its roots, and to find correct values for angles of incidence, at which the mode conversion occurs.

This paper presents a comprehensive study of a model called the ((2+1) {mathfrak {q}})-deformed tanh-Gordon model. This model is particularly useful for studying physical systems with violated symmetries, as it provides insights into their behavior. To solve the ((2+1) {mathfrak {q}})-deformed equation for specific parameter values, the (({mathfrak {H}}+frac{{mathcal {G}}^{prime }}{ {mathcal {G}}^{2}}))-expansion approach is employed. This technique generates analytical solutions that reveal valuable information about the system’s dynamics and behavior. These solutions offer insights into the underlying mathematics and deepen the understanding of the system’s properties. To validate the accuracy of the analytical solutions, the finite difference technique is also used to find a numerical solution to the ({mathfrak {q}})-deformed equation. This numerical approach ensures the correctness of the solutions and enhances the reliability of the results. Tables and graphics are presented in the publication to aid comprehension and comparison. These visuals improve the clarity and interpretability of the data, allowing readers to better understand the similarities and differences between the analytical and numerical solutions.

In this paper, we investigate a parabolic–parabolic–elliptic system that describes the initial stage of tumor-related angiogenesis, given by

We demonstrate that the model possesses a global classical solutions for all suitably regular initial data and associated homogeneous Neumann boundary conditions. Additionally, when m=1, the asymptotic behavior can be investigated.