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Based on the matrix block technique, the Deift-Zhou nonlinear steepest descent method is developed in order to study the asymptotic analysis of solutions of some nonlinear evolution equations associat...
In this talk, I will discuss the stability conditions for a free boundary problem of compressible Euler equations coupled with a nonlinear Poisson equation of electric potential. Under those stability...
Nonlinear partial differential equations (PDEs) are crucial to modelling important problems in science but they are computationally expensive and suffer from the curse of dimensionality. Since quantum...
Nonlinear Partial Differential Equations naturally appear in gas motions, fluid mechanics, differential geometry and many other fields, which cover compressible and incompressible Navier-Stokes equati...
This conference will demonstrate and strengthen connections between geometric analysis and nonlinear partial differential equations. We focus on new advances in several related themes, which include v...
Mathematical theory of continuum mechanics gives rise to important classes of nonlinear partial differential equations, such as the celebrated Euler and Navier-Stokes equations for both compressible a...
Nonlinear Partial Differential Equations naturally appear in gas motions, fluid mechanics, differential geometry and many other fields, which cover compressible and incompressible Navier-Stokes equati...
In keeping with the spirit of the Colston conference on Nonlinear Dynam- ics and Chaos, this chapter emphasizes ideas more than details, describing my vision of how the bifurcation theory of multipl...
Using the notion of fading memory, very strong versions of two theorems are proved. The first is that any time-invariant (TI) continuous nonlinear operator can be approximated by a Volterra series ope...
We consider nonlinear systems dx/dt=f(x(t)) where Df(x(t)) is known to lie in the convex hull of L n times n matrices A_1,ldots,A_L. For such systems, quadratic Lyapunov functions can be determined us...
We present a systematic treatment of efficient nonlinear optimization of queuing systems. The suite of formulations uses the computational tool of convex optimization, with fast polynomial time algori...
Topics: Modeling and analysis of nonlinear partial differential equations (especially reaction-diffusion type equations) in life sciences and other scientific disciplines. Focus on mathematical analys...
The focus of this dissertation is the existence, stability, and resulting dynamical evolution of localized stationary solutions to Nonlinear Schr¨odinger (NLS) equations with periodic confining potent...
In ecological population management, years of animal counts are fit to nonlinear, dynamic models (e.g. the Ricker model) because the values of the parameters are of interest. The yearly counts are sub...
Solitons confined in channels are studied in the two-dimensional nonlinear Schr\"odinger equation. We study the dynamics of two channel-guided solitons near the junction where two channels are merged....

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