Acta Applicandae Mathematicae最新文献

In the following paper, we have shown the existence and localization of solutions for a system of (n) third order differential equations under Sturm-Liouville type boundary conditions. Such systems appear in many physical problems, one of which is the jerk equations to locate the trajectory of a material point in space.

Motivated by singular limits for long-time optimal control problems, we investigate a class of parameter-dependent parabolic equations. First, we prove a turnpike result, uniform with respect to the parameters within a suitable regularity class and under appropriate bounds. The main ingredient of our proof is the justification of the uniform exponential stabilization of the corresponding Riccati equations, which is derived from the uniform null control properties of the model.

Then, we focus on a heat equation with rapidly oscillating coefficients. In the one-dimensional setting, we obtain a uniform turnpike property with respect to the highly oscillatory heterogeneous medium. Afterward, we establish the homogenization of the turnpike property. Finally, our results are validated by numerical experiments.

We extend our study of the swarm-based gradient descent method for non-convex optimization, (Lu et al., Swarm-based gradient descent method for non-convex optimization, 2022, arXiv:2211.17157), to allow random descent directions. We recall that the swarm-based approach consists of a swarm of agents, each identified with a position, (mathbf{x}), and mass, (m). The key is the transfer of mass from high ground to low(-est) ground. The mass of an agent dictates its step size: lighter agents take larger steps. In this paper, the essential new feature is the choice of direction: rather than restricting the swarm to march in the steepest gradient descent, we let agents proceed in randomly chosen directions centered around — but otherwise different from — the gradient direction. The random search secures the descent property while at the same time, enabling greater exploration of ambient space. Convergence analysis and benchmark optimizations demonstrate the effectiveness of the swarm-based random descent method as a multi-dimensional global optimizer.

In this paper, we mainly study the asymptotic monotonicity of positive solutions for fractional parabolic equation on the right half space. First, a narrow region principle for antisymmetric functions in unbounded domains is obtained, in which we remarkably weaken the decay condition (urightarrow 0) at infinity and only assume its growth rate does not exceed (|x|^{gamma }) ((0 < gamma < 2s)) compared with (Adv. Math. 377:107463, 2021). Then we obtain asymptotic monotonicity of positive solutions of fractional parabolic equation on (mathbb{R}^{N}_{+}times (0,infty )).

This paper is dedicated to the discussion of a new dynamical system involving a history-dependent variational-hemivariational inequality coupled with a non-linear evolution equation. The existence and uniqueness of the solution to this problem are established using the Rothe method and a surjectivity result for a pseudo-monotone perturbation of a maximal operator. Additionally, we derive the regularity solution for such a history-dependent variational-hemivariational inequality. Furthermore, the main results obtained in this study are applied to investigate the unique solvability of a dynamical viscoelastic frictional contact problem with long memory and wear.

We study the incompressible stationary Navier-Stokes equations in the upper-half plane with homogeneous Dirichlet boundary condition and non-zero external forcing terms. Existence of weak solutions is proved under a suitable condition on the external forces. Weak-strong uniqueness criteria based on various growth conditions at the infinity of weak solutions are also given. This is done by employing an energy estimate and a Hardy’s inequality. Several estimates of stream functions are carried out and two density lemmas with suitable weights for the homogeneous Sobolev space on 2-dimensional space are proved.

This article establishes the existence of global classical solutions to discrete coagulation equations with collisional breakage for collision kernels having linear growth. In contrast, the uniqueness is shown under additional restrictions on collision kernels. Moreover, mass conservation property and the positivity of solutions are also shown. While coagulation dominates, the occurrence of the gelation phenomenon for kernels having specific growth is also studied.

In this paper, we study the existence and regularity results for some parabolic equations with degenerate coercivity, and a singular right-hand side. The model problem is

where (Omega ) is a bounded open subset of (mathbb{R}^{N}) (Ngeq 2), (T>0), (Lambda in [0,p-1)), (f) is a non-negative function belonging to (L^{m}(Q_{T})), (Q_{T}=Omega times (0,T)), (partial Q_{T}=partial Omega times (0,T)), (0leq theta < p-1+frac{p}{N}+gamma (1+frac{p}{N})) and (0leq gamma < p-1).

We prove that the initial value problem with small data for the asymptotically flat spherically symmetric Einstein-Vlasov-Maxwell system admits the global in time solution in the case of the non-zero shift vector. This result extends the one already known for chargeless case.

In this paper, combining the non-decaying properties with the mixed-norm properties, the revelent sampling problems are studied under the target space of (L_{vec{p},frac{1}{omega }}(mathbb{R}^{d})). Firstly, we will give a stability theorem for the shift-invariant subspace (V_{vec{p},frac{1}{omega }}(varphi )). Secondly, an ideal sampling in (W_{vec{p},frac{1}{omega }}^{s}(mathbb{R}^{d})) is proved, and thirdly, a convergence theorem (or algorithm) is shown for (V_{vec{p},frac{1}{omega }}(varphi )). It should be pointed out that the auxiliary function (varphi ) enjoys the membership in a Wiener amalgam space.