A note on the axisymmetric diffusion equation

A note on unique solvability of the absolute value equation

It is proved that applying sufficient regularity conditions to the interval matrix $[A-|B|,A + |B|]$, we can create a new unique solvability condition for the absolute value equation $Ax + B|x|=b$, since regularity of interval matrices implies unique solvability of their corresponding absolute value equation. This condition is formulated in terms of positive deniteness of a certain point matrix...

A RESEARCH NOTE ON THE SECOND ORDER DIFFERENTIAL EQUATION

Let U(t, ) be solution of the Dirichlet problem y''+( t-q(t))y= 0 - 1 t l y(-l)= 0 = y(x), with variabIe t on (-1, x), for fixed x, which satisfies the initial condition U(-1, )=0 , (-1, )=1. In this paper, the asymptotic representation of the corresponding eigenfunctions of the eigen values has been investigated . Furthermore, the leading term of the asymptotic formula for ...

On the Axisymmetric Surface Diffusion Flow

A Note on the Degasperis-Procesi Equation

Indeed [1, 13, 15], both equations are bi-Hamiltonian and have an associated isospectral problem. Therefore they are both formally integrable (the integrability of (1.2) by means of the scattering/inverse scattering approach is discussed in [5, 9, 19]). Also, both equations admit exact peaked solitary wave solutions which have to be understood as weak solutions [10, 8, 22]. Moreover, using Kato...

A Note on Solving Prandtl's Integro-Differential Equation

A simple method for solving Prandtl's integro-differential equation is proposed based on a new reproducing kernel space. Using a transformation and modifying the traditional reproducing kernel method, the singular term is removed and the analytical representation of the exact solution is obtained in the form of series in the new reproducing kernel space. Compared with known investigations, its ...