A one-step new general mesh free scheme, which is based on radial basis functions, presented for a viscous wave equation with variable coefficients. By constructing simple extended function, it can be directly applied to propagation by using the strong form-based collocation method. There no need deal time-dependent particularly. Numerical results coefficients show that proposed method accurate...

The second elliptic equation method is a more general form of Jacobi function expansion method, which can obtain kinds solutions nonlinear evolution equation. In this paper, the used to solve Kdv-Burgers-Kuramoto (Benny) with variable coefficients, and its extremely rich solution properties are elucidated, among biperiodic solutions, solitary wave trigonometric periodic analyzed graphically.

In this paper, we study the exact boundary controllability of linear fourth-order Schrödinger equation, with variable physical parameters and clamped conditions on a bounded interval. The control acts first spatial derivative at right endpoint. We prove that system is exactly controllable any time $$T>0$$ . proofs are based detailed spectral analysis use nonharmonic Fourier series.

In this paper, we look for sufficient conditions on the lateral surface of the domain and on the coefficients of the boundary conditions of a N−space dimensional linear parabolic equation, in order to obtain existence, uniqueness and maximal regularity of the solution in a Hilbertian anisotropic Sobolev space when the right hand side of the equation is in a Lebesgue space. This work is an exten...