Search

The aim of this paper is twofold. The first aim is to describe the entire solutions of the partial differential equation (PDE) $u_{z_1}^2+2Bu_{z_1}u_{z_2}+u_{z_2}^2=e^g$, where B is a constant and g is a polynomial or an entire function in $\mathbb {C}^2$. The second aim is to consider the entire solutions of another PDE, which is a generalization of the well-known PDE of tubular surfaces.

The generalized Polynomial Chaos (gPC) method is one of the most widely used numerical methods for solving stochastic differential equations. Recently, attempts have been made to extend the the gPC to solve hyperbolic stochastic partial differential equations (SPDE). The convergence rate of the gPC depends on the regularity of the solution. It is shown that the characteristics technique can be used to derive general conditions for regularity of linear hyperbolic PDE, in a detailed case study of a linear wave equation with a random variable coefficient and random initial and boundary data.

Search Results

Refine search

Refine search

Actions for selected content:

2 results

Entire solutions of a variation of the eikonal equation and related PDEs

On Solution Regularity of Linear Hyperbolic Stochastic PDE Using the Method of Characteristics

Search Results

Refine search

Refine search

Actions for selected content:

Save Search

2 results

Entire solutions of a variation of the eikonal equation and related PDEs

On Solution Regularity of Linear Hyperbolic Stochastic PDE Using the Method of Characteristics