On a One-Dimensional Hydrodynamic Model for Semiconductors with Field-Dependent Mobility

We consider a one-dimensional, isentropic, hydrodynamical model for a unipolar semiconductor, with the mobility depending on the electric field. The mobility is related to the momentum relaxation time, and field-dependent mobility models are commonly used to describe the occurrence of saturation velocity, that is, a limit value for the electron mean velocity as the electric field increases. For the steady state system, we prove the existence of smooth solutions in the subsonic case, with a suitable assumption on the mobility function. Furthermore, we prove uniqueness of subsonic solutions for sufficiently small currents.

Existence and asymptotical behavior of solutions for a quasilinear Choquard equation with singularity

In this study, we consider the following quasilinear Choquard equation with singularity − Δ u + V ( x ) u − u Δ u 2 + λ ( I α ∗ ∣ u ∣ p ) ∣ u ∣ p − 2 u = K ( x ) u − γ , x ∈ R N , u > 0 , x ∈ R N , \left\{\begin{array}{ll}-\Delta u+V\left(x)u-u\Delta {u}^{2}+\lambda \left({I}_{\alpha }\ast | u{| }^{p})| u{| }^{p-2}u=K\left(x){u}^{-\gamma },\hspace{1.0em}& x\in {{\mathbb{R}}}^{N},\\ u\gt 0,\hspace{1.0em}& x\in {{\mathbb{R}}}^{N},\end{array}\right. where I α {I}_{\alpha } is a Riesz potential, 0 < α < N 0\lt \alpha \lt N , and N + α N < p < N + α N − 2 \displaystyle \frac{N+\alpha }{N}\lt p\lt \displaystyle \frac{N+\alpha }{N-2} , with λ > 0 \lambda \gt 0 . Under suitable assumption on V V and K K , we research the existence of positive solutions of the equations. Furthermore, we obtain the asymptotic behavior of solutions as λ → 0 \lambda \to 0 .

Existence, non-existence and blow-up behaviour of minimizers for the mass-critical fractional non-linear Schrödinger equations with periodic potentials

We consider the minimizing problem for the energy functional with prescribed mass constraint related to the fractional non-linear Schrödinger equation with periodic potentials. Using the concentration-compactness principle, we show a complete classification for the existence and non-existence of minimizers for the problem. In the mass-critical case, under a suitable assumption of the potential, we give a detailed description of blow-up behaviour of minimizers once the mass tends to a critical value.

Stability property of the prey free equilibrium point

We revisit a prey-predator model with stage structure for predator, which was proposed by Tapan Kumar Kar. By using the differential inequality theory and the comparison theorem of the differential equation, we show that the prey free equilibrium is globally asymptotically stable under some suitable assumption. Our study shows that although the predator species has other food resource, if the amount of the predator species is too large, it could also do irreversible harm to the prey species, and this could finally lead to the extinction of the prey species. Our result supplement and complement some known results.

Effective high-temperature estimates for intermittent maps

Using quantitative perturbation theory for linear operators, we prove a spectral gap for transfer operators of various families of intermittent maps with almost constant potentials (‘high-temperature’ regime). Hölder and bounded $p$-variation potentials are treated, in each case under a suitable assumption on the map, but the method should apply more generally. It is notably proved that for any Pommeau–Manneville map, any potential with Lipschitz constant less than 0.0014 has a transfer operator acting on $\operatorname{Lip}([0,1])$ with a spectral gap; and that for any two-to-one unimodal map, any potential with total variation less than 0.0069 has a transfer operator acting on $\operatorname{BV}([0,1])$ with a spectral gap. We also prove under quite general hypotheses that the classical definition of spectral gap coincides with the formally stronger one used in Giulietti et al [The calculus of thermodynamical formalism. J. Eur. Math. Soc., to appear. Preprint, 2015, arXiv:1508.01297], allowing all results there to be applied under the high-temperature bounds proved here: analyticity of pressure and equilibrium states, central limit theorem, etc.

Mapping of b-Value Anomalies Along the Strike-Slip Fault System on the Thailand–Myanmar Border: Implications for Upcoming Earthquakes

In order to determine the prospective areas of the forthcoming earthquake sources, the [Formula: see text]-values of the frequency-magnitude earthquake distributions were analyzed spatially and mapped along the strike-slip fault system at the Thailand–Myanmar border. In order to constrain the relationship between the variation of [Formula: see text] and the following hazardous earthquake, the completeness of earthquake catalogue was manipulated into two datasets for (i) 1980–2000 and (ii) 1980–2005 and the [Formula: see text]-values mapped. Utilizing the suitable assumption of 30 fixed earthquake events, the following [Formula: see text] earthquakes illustrate a significant relation between their epicenter and the areas showing relatively low [Formula: see text]-values. By utilizing the most recent earthquake data (1980–2015), five areas exhibiting low [Formula: see text]-values (implying prospective earthquake sources) can be identified along the strike-slip fault system. Compared with earthquake activities evaluated previously along the strike-slip fault system, the data reveal that these five areas may potentially generate earthquakes up to 7.0[Formula: see text][Formula: see text] within the coming 50 years; the recurrence of the [Formula: see text]-5.0 earthquake is about 10 years and the probabilities of the [Formula: see text]-5.0 earthquake are about 40–95%, respectively. Since these prospective hazardous seismic zones are located close to cities, population centers and hydropower dams, an effective mitigation plan should be developed.

Pseudofinite structures and simplicity

We explore a notion of pseudofinite dimension, introduced by Hrushovski and Wagner, on an infinite ultraproduct of finite structures. Certain conditions on pseudofinite dimension are identified that guarantee simplicity or supersimplicity of the underlying theory, and that a drop in pseudofinite dimension is equivalent to forking. Under a suitable assumption, a measure-theoretic condition is shown to be equivalent to local stability. Many examples are explored, including vector spaces over finite fields viewed as 2-sorted finite structures, and homocyclic groups. Connections are made to products of sets in finite groups, in particular to word maps, and a generalization of Tao's Algebraic Regularity Lemma is noted.

Mapping b-Value Anomalies Along the Indonesian Island Chain: Implications for Upcoming Earthquakes

In this study, the geospatial frequency–magnitude distribution (FMD) b-value images of the prospect sources of upcoming earthquakes were investigated along the Indonesian Sunda Margin (ISM) that strikes parallel to and near the Indonesian Island chain. After enhancing the completeness and stability of the earthquake catalogue, the seismicity data were separated according to their seismotectonic setting into shallow crustal and Intraslab earthquakes. In order to verify the spatial relationship between the b-values and the occurrence of subsequent major earthquakes, the complete shallow crustal seismicity dataset (1980–2005) was truncated into the 1980–2000 sub-dataset. Utilizing the suitable assumption of fixed-number of earthquakes, retrospective tests of both the complete and truncated datasets supported that areas of comparatively low b-values could reasonably be expected to predict likely hypocenters of future earthquakes. As a result, the present-day distributions of b-values derived from the complete (1980–2005) shallow crustal and Intraslab seismicity datasets revealed eight and six earthquake-prone areas, respectively, along the ISM. Since most of these high risk areas proposed here are quite close to the major cities of Indonesia, attention should be paid and mitigation plans should be developed for both seismic and tsunami hazards.

Boundary Stabilization of the Wave Equation with Time-Varying and Nonlinear Feedback

We study the stabilization of the wave equation with variable coefficients in a bounded domain and a time-varying and nonlinear term. By the Riemannian geometry methods and a suitable assumption of nonlinearity and the time-varying term, we obtain the uniform decay of the energy of the system.

Existence and Uniqueness of Solution for Perturbed Nonautonomous Systems with Nonuniform Exponential Dichotomy

Nonuniform exponential dichotomy has been investigated extensively. The essential condition of these previous results is based on the assumption that the nonlinear term satisfies|f(t,x)|≤μe−ε|t|. However, this condition is very restricted. There are few functions satisfying|f(t,x)|≤μe−ε|t|. In some sense, this assumption is not reasonable enough. More suitable assumption should be|f(t,x)|≤μ. To the best of the authors' knowledge, there is no paper considering the existence and uniqueness of solution to the perturbed nonautonomous system with a relatively conservative assumption|f(t,x)|≤μ. In this paper, we prove that if the nonlinear term is bounded, the perturbed nonautonomous system with nonuniform exponential dichotomy has a unique solution. The technique employed to prove Theorem 4 is the highlight of this paper.