Acta Mathematica Scientia最新文献

In this paper, we establish some regularity conditions on the density and velocity fields to guarantee the energy conservation of the weak solutions for the three-dimensional compressible nematic liquid crystal flow in the periodic domain.

Drug resistance is one of the most intractable issues in targeted therapy for cancer diseases. It has also been demonstrated to be related to cancer heterogeneity, which promotes the emergence of treatment-refractory cancer cell populations. Focusing on how cancer cells develop resistance during the encounter with targeted drugs and the immune system, we propose a mathematical model for studying the dynamics of drug resistance in a conjoint heterogeneous tumor-immune setting. We analyze the local geometric properties of the equilibria of the model. Numerical simulations show that the selectively targeted removal of sensitive cancer cells may cause the initially heterogeneous population to become a more resistant population. Moreover, the decline of immune recruitment is a stronger determinant of cancer escape from immune surveillance or targeted therapy than the decay in immune predation strength. Sensitivity analysis of model parameters provides insight into the roles of the immune system combined with targeted therapy in determining treatment outcomes.

In this paper, we are concerned with solutions to the fractional Schrödinger-Poisson system

with prescribed mass (int_{{mathbb{R}^3}} {|u{|^2}{rm{d}}x = {a^2}} ), where a > 0 is a prescribed number, μ > 0 is a paremeter, s ∈ (0, 1), 2 < q < 2*_s, and (2_s^ * = {6 over {3 - 2s}}) is the fractional critical Sobolev exponent. In the L²-subcritical case, we show the existence of multiple normalized solutions by using the genus theory and the truncation technique; in the L²-supercritical case, we obtain a couple of normalized solutions by developing a fiber map. Under both cases, to recover the loss of compactness of the energy functional caused by the doubly critical growth, we need to adopt the concentration-compactness principle. Our results complement and improve upon some existing studies on the fractional Schrödinger-Poisson system with a nonlocal critical term.

In this paper, we are concerned with a three-dimensional non-isothermal model for the compressible nematic liquid crystal flows in a periodic domain. Under some smallness and structural assumptions imposed on the time-periodic force, we establish the existence of the time-periodic solutions to the system by using a regularized approximation scheme and the topological degree theory. We also prove a uniqueness result via energy estimates.

This paper deals with the problem of limit cycles for the whirling pendulum equation ẋ = y, ẏ = sin x(cos x − r) under piecewise smooth perturbations of polynomials of cos x, sin x and y of degree n with the switching line x = 0. The upper bounds of the number of limit cycles in both the oscillatory and the rotary regions are obtained using the Picard-Fuchs equations, which the generating functions of the associated first order Melnikov functions satisfy. Furthermore, the exact bound of a special case is given using the Chebyshev system. At the end, some numerical simulations are given to illustrate the existence of limit cycles.

This paper is concerned with the minimizers of L²-subcritical constraint variational problems with spatially decaying nonlinearities in a bounded domain Ω of ℝ^N (N ≥ 1). We prove that the problem admits minimizers for any M > 0. Moreover, the limiting behavior of minimizers as M → ∞ is also analyzed rigorously.

Discrete feedback control was designed to stabilize an unstable hybrid neutral stochastic differential delay system (HNSDDS) under a highly nonlinear constraint in the H_∞ and exponential forms. Nevertheless, the existing work just adapted to autonomous cases, and the obtained results were mainly on exponential stabilization. In comparison with autonomous cases, non-autonomous systems are of great interest and represent an important challenge. Accordingly, discrete feedback control has here been adjusted with a time factor to stabilize an unstable non-autonomous HNSDDS, in which new Lyapunov-Krasovskii functionals and some novel technologies are adopted. It should be noted, in particular, that the stabilization can be achieved not only in the routine H_∞ and exponential forms, but also the polynomial form and even a general form.

We consider dual Toeplitz operators on the orthogonal complements of the Fock-Sobolev spaces of all nonnegative real orders. First, for symbols in a certain class containing all bounded functions, we study the problem of when an operator which is finite sums of the dual Toeplitz products is compact or zero. Next, for bounded symbols, we construct a symbol map and exhibit a short exact sequence associated with the C^*-algebra generated by all dual Toeplitz operators with bounded symbols.

The nonlinear stability of plane parallel shear flows with respect to tilted perturbations is studied by energy methods. Tilted perturbation refers to the fact that perturbations form an angle (theta in (0,{pi over 2})) with the direction of the basic flows. By defining an energy functional, it is proven that plane parallel shear flows are unconditionally nonlinearly exponentially stable for tilted streamwise perturbation when the Reynolds number is below a certain critical value and the boundary conditions are either rigid or stress-free. In the case of stress-free boundaries, by taking advantage of the poloidal-toroidal decomposition of a solenoidal field to define energy functionals, it can be even shown that plane parallel shear flows are unconditionally nonlinearly exponentially stable for all Reynolds numbers, where the tilted perturbation can be either spanwise or streamwise.

In this paper, we consider a class of third-order nonlinear delay dynamic equations. First, we establish a Kiguradze-type lemma and some useful estimates. Second, we give a sufficient and necessary condition for the existence of eventually positive solutions having upper bounds and tending to zero. Third, we obtain new oscillation criteria by employing the Pötzsche chain rule. Then, using the generalized Riccati transformation technique and averaging method, we establish the Philos-type oscillation criteria. Surprisingly, the integral value of the Philos-type oscillation criteria, which guarantees that all unbounded solutions oscillate, is greater than θ₄(t₁, T). The results of Theorem 3.5 and Remark 3.6 are novel. Finally, we offer four examples to illustrate our results.