Acta Applicandae Mathematicae最新文献

We are focused on solving a general class of bilevel variational inequalities involving quasimonotone operators in real Hilbert spaces. A strong convergent iterative method for solving the problem is presented and analysed. Our work generalizes several existing results in the literature and holds two major mathematical advantages. 1) Any generated sequence by the algorithm preserves the Fejér monotonicity property; and 2) There is no need to execute a line-search or know a-prior the strongly monotone coefficient or Lipschitz constant. Numerical experiments with comparisons to existing/related methods illustrate the performances of the proposed method and in particular, application to optimal control problems suggests the practical potential of our scheme.

This paper deals with the limiting behavior of nonlocal stochastic Schrödinger lattice systems with time-varying delays and multiplicative noise in weighted space. We first consider the existence and uniqueness of tempered pullback random attractors for considered stochastic system and then establish the upper-semicontinuity of these attractors when the length of time delay approaches zero.

We present an innovative approach to dimensional analysis, referred to as augmented dimensional analysis and based on a representation theorem for complete quantity functions with a scaling-covariant scalar representation. This new theorem, grounded in a purely algebraic theory of quantity spaces, allows the classical (pi ) theorem to be restated in an explicit and precise form and its prerequisites to be clarified and relaxed. Augmented dimensional analysis, in contrast to classical dimensional analysis, is guaranteed to take into account all relations among the quantities involved. Several examples are given to show that the information thus gained, together with symmetry assumptions, can lead to new or stronger results. We also explore the connection between dimensional analysis and matroid theory, elucidating combinatorial aspects of dimensional analysis. It is emphasized that dimensional analysis rests on a principle of covariance.

In this paper, we study the long time behavior of solutions for an optimal control problem associated with the magnetic Bénard problem in a two dimensional bounded domain, achieved through the adjustment of distributed controls. We first construct a quasi-optimal solution for the magnetic Bénard problem characterized by exponential decay over time. We then derive preliminary estimates concerning the extended temporal behavior of all admissible solutions to the magnetic Bénard problem. Next we establish the existence of a solution for the optimal control problem over both finite and infinite time intervals. Additionally, we present the first-order necessary optimality conditions for the finite time interval case. Finally, we establish the long-time decay characteristics of the solutions for the optimal control problem.

This paper is concerned with the study of a nonlinear non-local equation that has a commutator structure. The equation reads

with (sin (0, 1]). We are interested in solutions stemming from periodic positive bounded initial data. The given function (Fin mathcal{C}^{infty }(mathbb{R}^{+})) must satisfy (F'>0) a.e. on ((0, +infty )). For instance, all the functions (F(u)=u^{n}) with (nin mathbb{N}^{ast }) are admissible non-linearities. The local theory can also be developed on the whole space, however the most complete well-posedness result requires the periodic setting. We construct global classical solutions starting from smooth positive data, and global weak solutions starting from positive data in (L^{infty }). We show that any weak solution is instantaneously regularized into (mathcal{C}^{infty }). We also describe the long-time asymptotics of all solutions. Our methods follow several recent advances in the regularity theory of parabolic integro-differential equations, in particular (Ann. Fac. Sci. Toulouse, Math. 25(4):723–758, 2016; Ann. Fac. Sci. Toulouse, Math. 27(4):667–677, 2018).

We consider the stability of the global weak solution of the Quantum Euler system in two space dimensions. More precisely, we establish compactness properties of global finite energy weak solution for large initial data provided that these are axisymmetric. The main novelty is that the initial velocity is not necessary irrotational when the density is not vanishing, our main argument is based on the Madelung transform which enables us to prove new Kato estimates on the irrotational part of the velocity.

The non-linear collision-induced breakage equation has significant applications in particulate processes. Two semi-analytical techniques, namely homotopy analysis method (HAM) and accelerated homotopy perturbation method (AHPM) are investigated along with the well-known numerical scheme finite volume method (FVM) to comprehend the dynamical behavior of the non-linear system, i.e., the concentration function, the total number, total mass and energy dissipation of the particles in the system. These semi-analytical methods provide approximate analytical solutions by truncating the infinite series form. The theoretical convergence analyses of the series solutions of HAM and AHPM are discussed under some assumptions on the collisional kernels. In addition, the error estimations of the truncated solutions of both methods equip the maximum absolute error bound. Moreover, HAM simulations are computationally costly compared to AHPM because of an additional auxiliary parameter. To justify the applicability and accuracy of these series methods, approximated solutions are compared with the findings of FVM and analytical solutions considering three physical problems.

In this paper, a critical fourth-order Kirchhoff type elliptic equation with a subcritical perturbation is studied. The main feature of this problem is that it involves both a nonlocal coefficient and a critical term, which bring essential difficulty for the proof of the existence of weak solutions. When the dimension of the space is smaller than or equals to 7, the existence of weak solution is obtained by combining the Mountain Pass Lemma with some delicate estimate on the Talenti’s functions. When the dimension of the space is larger than or equals to 8, the above argument no longer works. By introducing an appropriate truncation on the nonlocal coefficient, it is shown that the problem admits a nontrivial solution under appropriate conditions on the parameter.

In this paper, we are concerned with the three-dimensional nonhomogeneous Bénard system with density-dependent viscosity in bounded domain. The global well-posedness of strong solution is established, provided that the initial total mass (|rho _{0}|_{L^{1}}) is suitably small. In particular, the initial velocity and temperature can be arbitrarily large. Moreover, the exponential decay of strong solution is also obtained. It is worth noting that the vacuum of initial density is allowed.

A functional Hilbert space is the Hilbert space ℋ of complex-valued functions on some set (Theta subseteq mathbb{C}) such that the evaluation functionals (varphi _{tau }left ( fright ) =fleft ( tau right ) ), (tau in Theta ), are continuous on ℋ. The Berezin number of an operator (X) is defined by (mathbf{ber}(X)=underset{tau in {Theta } }{sup }big vert widetilde{X}(tau )big vert = underset{tau in {Theta } }{sup }big vert langle Xhat{k}_{tau },hat{k}_{tau }rangle big vert ), where the operator (X) acts on the reproducing kernel Hilbert space ({mathscr{H}}={mathscr{H}(}Theta )) over some (non-empty) set (Theta ). In this paper, we introduce a new family involving means (Vert cdot Vert _{sigma _{t}}) between the Berezin radius and the Berezin norm. Among other results, it is shown that if (Xin {mathscr{L}}({mathscr{H}})) and (f), (g) are two non-negative continuous functions defined on ([0,infty )) such that (f(t)g(t) = t,,(tgeqslant 0)), then

and

where (sigma ) is a mean dominated by the arithmetic mean (nabla ).