Many applications involve hyperbolic systems of conservation laws with source terms. The numerical solution of such systems may be challenging, especially when the source terms are stiff. Uniform accuracy with respect to the stiffness parameter is a highly desirable property but it is, in general, very difficult to achieve using underresolved discretizations. For such problems we develop differ...

In this work, we employ the $${\bar{\partial }}$$ -steepest descent method to investigate Cauchy problem of Wadati–Konno–Ichikawa (WKI) equation with initial conditions in weighted Sobolev space $${\mathcal {H}}({\mathbb {R}})$$ . The long time asymptotic behavior solution q(x, t) is derived a fixed space-time cone $$S(y_{1},y_{2},v_{1},v_{2})=\{(y,t)\in {\mathbb {R}}^{2}: y=y_{0}+vt, ~y_{0}\in...

Consider the energy-critical focusing wave equation in odd space dimension $N\geq 3$. The has a nonzero radial stationary solution $W$, which is unique up to scaling and sign change. In this paper we prove that any radial, bounded energy norm of behaves asymptotically as sum modulated $W$s, decoupled by scaling, radiation term. The proof essentially boils down fact does not have purely nonrad...

Purpose – We analyze the effects of leadership on work-family spillovers. Specifically, we analyze the relationships between leadership (leader-member exchange, LMX) with one negative work-family spillover effect (work-family interference) and one positive work-family spillover effect (work-family facilitation). We hypothesize that LMX influences work-family spillover via different mediators, r...

Successful prediction of groundwater flow and solute transport through highly heterogeneous aquifers has remained elusive due to the limitations of methods to characterize hydraulic conductivity (K) and generate realistic stochastic fields from such data. As a result, many studies have suggested that the classical advective-dispersive equation (ADE) cannot reproduce such transport behavior. Her...

We describe the dispersive and nonlinear optical properties of microresonator-modified waveguides. While many applications of microresonators demand ultra-high quality factors and as a result impose strict fabrication tolerances, we examine a variety of useful devices that may be may be constructed using small numbers of only moderately-high Q resonators using the current state of the art in fa...