Search results for "method of characteristic"

A Study on the Propagation of Plane Stress Waves across the Thickness of a Plate by the Method of Analytic Continuation in Time

2004

The interaction of plane tension/compression waves propagating within a plate perpendicularly to its surface is considered. The analytic solution is obtained by a modified method of characteristics for the one-dimensional wave equation used in problems on an impact of a rigid body on the surface of a plate. The displacements, velocities, and stresses in the plate are determined by the edge disturbance caused by the initial velocity and the stationary force field of masses of the striker and the plate. The method of analytic continuation in time put forward allows a stress analysis for an arbitrary time interval by using finite expressions. Contrary to a stress analysis in the frequency doma…

Shock formation in the dispersionless Kadomtsev-Petviashvili equation

2016

The dispersionless Kadomtsev-Petviashvili (dKP) equation $(u_t+uu_x)_x=u_{yy}$ is one of the simplest nonlinear wave equations describing two-dimensional shocks. To solve the dKP equation we use a coordinate transformation inspired by the method of characteristics for the one-dimensional Hopf equation $u_t+uu_x=0$. We show numerically that the solutions to the transformed equation do not develop shocks. This permits us to extend the dKP solution as the graph of a multivalued function beyond the critical time when the gradients blow up. This overturned solution is multivalued in a lip shape region in the $(x,y)$ plane, where the solution of the dKP equation exists in a weak sense only, and a…

Global integrability of the gradients of solutions to partial differential equations

1994

Modelling analysis of distribution network filling process during intermittent supply

2009

The paper presents the modeling results of the filling process of a water distribution network subjected to intermittent supply. The local tanks built by users for reducing their vulnerability to intermittent supply increase user water demand at the beginning of the service period and the time required for completely fill the network. Such a delicate process is responsible of the inequalities taking part among users. Users located in advantaged positions can receive water resources soon after the beginning of the service period while disadvantaged users have to wait until the network is full. Such an highly dynamic process requires ad-hoc models to be developed in order to obtain reliable r…