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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...
Whether the 3D incompressible Euler equations can develop a finite-time singularity from smooth initial data is an outstanding open problem. In this talk, we will first review recent progress in singu...
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...
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...
The KdV equation can be considered as a special case of the general equationutCf .u/x−g.uxx/x D 0;> 0;wheref is non-linear andg is linear, namelyf .u/ D u2=2 andg.v/ D v. As the parameter  t...
We introduce a nonlinear dispersive quintic equation. Its travelling waves are governed by a linear equation. We construct a large variety of explicit compact solitary waves with one or many humps. So...
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...
Recently, Holm and Ivanov, proposed and studied a class of multi-component generalisations of the Camassa-Holm equations [D D Holm and R I Ivanov, Multi-component generalizations of the CH equation: g...
We define a new grading, that we call the "level grading", on the algebra of polynomials generated by the derivatives $u_{k+i}=\partial^{k+i}u/\partial x^{k+i}$ over the ring $K^{(k)}$ of $C^{\infty}$...
We study the periodic homogenization of u"−c( x" ) Zz∈RN [u"(x+z)−u"(x)−1|z|<1h∇u"(x).
We develop a well-posedness theory for second order systems in bounded domains where boundary phenomena like glancing and surface waves play an important role. Attempts have previ- ously been made t...
The main goal of this paper is to study the nature of the support of the solution of suitable nonlinear Schrodinger equations mainly the compactness of the support and its spatial localization.

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