Probabilistic approach to wave propagation problems II: Boundary value problems

L2-transforms for boundary value problems

In this article, we will show the complex inversion formula for the inversion of the L2-transform and also some applications of the L2, and Post Widder transforms for solving singular integral equation with trigonometric kernel. Finally, we obtained analytic solution for a partial differential equation with non-constant coefficients.

A numerical approach to solve eighth order boundary value problems by Haar wavelet collocation method

In this paper a robust and accurate algorithm based on Haar wavelet collocation method (HWCM) is proposed for solving eighth order boundary value problems. We used the Haar direct method for calculating multiple integrals of Haar functions. To illustrate the efficiency and accuracy of the concerned method, few examples are considered which arise in the mathematical modeling of fluid dynamics an...

Propagation of Singularities of Solutions to Semilinear Boundary Value Problems

Let P be a second-order, strictly hyperbolic differential operator on an open region Q C R n (n > 3) with smooth noncharacteristic boundary. Given a solution u G fffoc(n), s > (n + l ) /2 , to Pu = f(x,u), we discuss the propagation of microlocal H singularities in the range s < r < 2s — n/2 in the general case where the Hamilton field of p may be tangent to dT* f2\0 to arbitrarily high finite ...

Approximating Initial-Value Problems with Two-Point Boundary-Value Problems: BBM-Equation

Initial Value/boundary Value Problems for Fractional Diffusion-wave Equations and Applications to Some Inverse Problems

We consider initial value/boundary value problems for fractional diffusion-wave equation: ∂ α t u(x, t) = Lu(x, t), where 0 < α ≤ 2, where L is a symmetric uniformly elliptic operator with t-independent smooth coefficients. First we establish the unique existence of ths weak solutions and the asymptotic behaviour as the time t goes to ∞ and the proofs are based on the eigenfunction expansions. ...