Applied Mathematics Letters最新文献

In this paper we consider a system describing a quantum particle self interacting with the Born Infeld electromagnetic field. The existence of a radial ground state solution is proved in the attractive case.

Investigations on the real world have been facilitating the development of nonlinear science, and today, fluid dynamics and plasma physics attract people’s attention. This Letter studies a (2+1)-dimensional variable-coefficient Sawada-Kotera system in plasma physics and fluid dynamics. We build up a family of the similarity reductions, connecting that system with a known ordinary differential equation. Our similarity reductions depend on the plasma/fluid variable coefficients in that system, under certain variable-coefficient constraints.

We study the linear elasticity system under singular forces. We show the existence and uniqueness of solutions in two frameworks: weighted Sobolev spaces $H^1(\varpi ,\Omega )$, where the weight belongs to the Muckenhoupt class $A_2$, and standard Sobolev spaces $W^{1,p}\left(\Omega \right)$, where the integrability index $p$ is less than $d/(d-1)$. We also propose a standard finite element scheme and provide optimal error estimates in the $L^2$–norm.

For solving the system of tensor equations $A{x}^{m-1}=b$, where $\mathrm{x,b}\in R^n$ and $A$ is an $m$-order $n$-dimensional real tensor, we introduce two greedy Kaczmarz-type methods: the tensor relaxed greedy randomized Kaczmarz algorithm and the accelerated tensor relaxed greedy Kaczmarz algorithm. The deterministic convergence analysis of both methods is given based on the local tangential cone condition. Numerical results demonstrate that the greedy Kaczmarz-type methods are more efficient than the randomized Kaczmarz-type methods, and the accelerated greedy version exhibits significant acceleration.

This paper is concerned with the following Hamiltonian elliptic system $\left(\begin{array}{c}-\Delta u+\overrightarrow{b}\left(x\right)\cdot \nabla u+V\left(x\right)u=H_v(x,u,v)in{R}^N,\\ -\Delta v-\overrightarrow{b}\left(x\right)\cdot \nabla v+V\left(x\right)v=H_u(x,u,v)in{R}^N.\end{array}\right)$Under a subquadratic growth condition on the nonlinearity, we establish the existence of a sequence of small energy solutions by using a new critical point theorem for strongly indefinite functional.

This paper explores the dynamics of a diffusive predator–prey model, considering schooling behavior and Smith growth in prey. Initially, we have formulated the pertinent characteristic equations. Subsequently, We proceed to examine the existence of the Turing bifurcation and Hopf bifurcation, phenomena that describe the emergence of spatial and temporal patterns due to diffusion and oscillations, respectively, and focusing on the parameters of the intrinsic growth rate $\gamma$ and the diffusion coefficient $d_2$ of the prey. Finally, we conduct numerical simulations to validate our theoretical findings and further illustrate the dynamics of the predator–prey system, considering schooling behavior and Smith growth in prey.

By applying the minimum residual technique to the shift-splitting (SS) iteration scheme, we introduce a non-stationary iteration method named minimum residual SS (MRSS) iteration method to solve non-Hermitian positive definite and positive semidefinite systems of linear equations. Theoretical analyses show that the MRSS iteration method is unconditionally convergent for both of the two kinds of systems of linear equations. Numerical examples are employed to verify the feasibility and effectiveness of the MRSS iteration method.

The Dahlquist barrier states that the highest attainable order for an A-stable linear multistep method is limited to 2. In this paper, we adopt the deferred correction approach with the BDF methods to develop A-stable third and fourth-order multistep methods with low stages. The stability of the methods is investigated to show how A-stability can be achieved. Numerical experiments are conducted to validate the accuracy and stability of the proposed methods when applied to stiff problems.

Using topological transversality method together with barrier strip technique and cut-off technique, we obtain new existence and uniqueness results of radial solutions to the Neumann problems involving prescribed mean curvature operator $\left(\begin{array}{c}\text{div}\left(\frac{\nabla v}{\sqrt{1+{|\nabla v|}^2}}\right)=f\left(\left|x\right|,v,\frac{dv}{dr}\right)in\Omega ,\\ \frac{\partial v}{\partial n}=0on\partial \Omega ,\end{array}\right)$where $\Omega =\{x\in R^N:R_1<\left|x\right|<R_2\}(0\le R_1<R_2,N\ge 2)$, $f:[R_1,R_2]\times R^2\to R$ is continuous. Meanwhile, we demonstrate the importance of our results through an illustrative example.