‎In this paper we focus on the Cauchy problem for the generalized‎ ‎IBq equation with damped term in $n$-dimensional space‎. ‎We establish the global existence and decay estimates of solution with $L^q(1leq qleq 2)$ initial value‎, ‎provided that the initial value is suitably small‎. ‎Moreover‎, ‎we also show that the solution is asymptotic to the solution $u_L$ to the corresponding linear equa...

Perturbative renormalization group theory is developed as a unified tool for global asymptotic analysis. With numerous examples, we illustrate its application to ordinary differential equation problems involving multiple scales, boundary layers with technically difficult asymptotic matching, and WKB analysis. In contrast to conventional methods, the renormalization group approach requires neith...

We investigate the effects of feedback on a decentralized detection system consisting of N sensors and a detection center. It is assumed that observations are independent and identically distributed across sensors, and that each sensor compresses its observations into a fixed number of quantization levels. We consider two variations on this setup. One entails the transmission of sensor data to ...

In this paper, finite difference schemes based on asymptotic analysis and the augmented immersed interface method are proposed for potential problems with an inclusion whose characteristic width is much smaller than the characteristic length in one and two dimensions. We call such a problem as a crack problem for simplicity. In the proposed methods, we use asymptotic analysis to approximate the...

The following problem arose in connection with our research in statistical group theory: estimate a, := the number of partitions of n into parts that are pairwise relatively prime. This differs from most problems in the theory of partitions because of the complicated relationship between the part sixes. We obtain an asymptotic formula for log a,, but leave open the challenging task of obtaining...

We establish a heavy-traffic asymptotic expansion (in powers of one minus the traffic intensity) for the asymptotic decay rates of queue-length and workload tail probabilities in stable infinite-capacity multi-channel queues. The specific model has multiple independent heterogeneous servers, each with i.i.d. service times, that are independent of the arrival process, which is the superposition ...