arXiv subjects

Juan-Ming Yuan

Publications and source records attributed to Juan-Ming Yuan.

4 recordsLinked to original sources

arXiv2015

Well-posedness of the two-dimensional generalized Benjamin-Bona-Mahony equation on the upper half plane

This paper focuses on the two-dimensional Benjamin-Bona-Mahony and Benjamin-Bona-Mahony-Burgers equations with a general flux function. The aim is at the global (in time) well-posedness of the initial-and boundary-value problem for these equations defined in the upper half-plane. Under suitable growth conditions on the flux function, we are able to establish the global well-posedness in a Sobolev class. When the initial- and boundary-data become more regular, the corresponding solutions are shown to be classical. In addition, the continuous dependence on the data is also obtained.

math.AP↗

arXiv2009

Complex-valued Burgers and KdV-Burgers equations

Spatially periodic complex-valued solutions of the Burgers and KdV-Burgers equations are studied in this paper. It is shown that for any sufficiently large time T, there exists an explicit initial data such that its corresponding solution of the Burgers equation blows up at T. In addition, the global convergence and regularity of series solutions is established for initial data satisfying mild conditions.

math.AP↗

arXiv2008

A new solution representation for the BBM equation in a quarter plane and the eventual periodicity

The initial- and boundary-value problem for the Benjamin-Bona-Mahony (BBM) equation is studied in this paper. The goal is to understand the periodic behavior (termed as eventual periodicity) of its solutions corresponding to periodic boundary condition or periodic forcing. To this aim, we derive a new formula representing solutions of this initial- and boundary-value problem by inverting the operator $\partial_t +α\partial_x -γ\partial_{xxt}$ defined in the space-time quarter plane. The eventual periodicity of the linearized BBM equation with periodic boundary data and forcing term is established by combining this new representation formula and the method of stationary phase.

math.AP↗

arXiv2003

Classification of Steadily Rotating Spiral Waves for the Kinematic Model

Spiral waves arise in many biological, chemical, and physiological systems. The kinematical model can be used to describe the motion of the spiral arms approximated as curves in the plane. For this model, there appeared some results in the literature. However, these results all are based upon some simplification on the model or prior phenomenological assumptions on the solutions. In this paper, we use really full kinematic model to classify a generic kind of steadily rotating spiral waves, i.e., with positive (or negative) curvature. In fact, using our results (Theorem 8), we can answer the following questions: Is there any steadily rotating spiral wave for a given weakly excitable medium? If yes, what kind of information we can know about these spiral waves? e.g., the tip's curvature, the tip's tangential velocity, and the rotating frequency. Comparing our results with previous ones in the literature, there are some differences between them. There are only solutions with monotonous curvatures via simplified model but full model admits solutions with any given oscillating number of the curvatures.

math.DS↗