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Banach Spaces of Solutions of the Helmholtz Equation in the Plane


Time Decay and Regularity of Solutions to the Wave Equation


Mapping Properties of a Projection Related to the Helmholtz Equation


Herglotz Wave Functions are the entire solutions of the Helmholtz equation which have L2FarFieldPattern.


The Ces\'aro operator $\mathcal{C}_{\alpha}$ is defined by \begin{equation*} (\mathcal{C}_{\alpha}f)(x) = \int_{0}^{1}t^{1}f\left( t^{1}x \right)\alpha (1t)^{\alpha 1}\,dt~, \end{equation*} where $f$ denotes a function on $\mathbb{R}$.


On Global Finite Energy Solutions of the CamassaHolm Equation


We consider the CamassaHolm equation with data in the energy norm H1(R1).


Sharp Global WellPosedness for a Higher Order Schrodinger Equation


It is transferred to a boundary value problem for analytic functions and then further reduced to a singular integral equation, the unique solvability and an effective method of solution for which are established.


This paper provides a functional equation satisfied by the dichromatic sum function of rooted outerplanar maps.


By the equation, the dichromatic sum function can be found explicitly.


By means of our inequality and the method of Lyapunov function we study the stability of two kinds of large scale differential systems with time lag and the stability of a higherorder differential equation with time lag.


The Alternating Segment CrankNicolson scheme for onedimensional diffusion equation has been developed in [1], and the Alternating Block CrankNicolson method for twodimensional problem in [2].


In this paper for the twodimensional diffusion equation, the net region is divided into bands, a special kind of block.


The errors estimation of the Chebyshev spectraldifference method for twodimensional vorticity equation


We construct a Chebyshev spectraldifference scheme for solving twodimensional vorticity equation with semihomogeneous boundary conditions.


The chebyshev spectral method with a restraint operator for burgers equation


For a differential equation, a theoretical proof of the relationship between the symmetry and the oneparameter invariant group is given: the relationship between symmetry and the groupinvariant solution is presented.


As an application, some solutions of theKdV equation are discussed.


Exact envelope wave solution to nonlinear Schr?dinger equation with dissipative term

