Year of Graduation
Front Tracking Method from the Viewpoint of Nonlinear Waves Interaction
Mathematical Methods of Natural Sciences and Computer Technologies
In this work, the problem of approximating the solution of the Cauchy problem for the Hopf equation by means of a step function is considered. Properties of the auxiliary switch function are studied, as well as the weak approximation of a product of Heaviside functions. Simple examples of the Cauchy problem with step functions with two, three and four jumps in the initial condition are considered. These results are then generalized to an arbitrary number of jumps, which allows them to be used in the study of the Cauchy problem with an arbitrary measurable bounded function as the initial condition. A theorem on global solvability, in the class of piecewise-differentiable functions with a finite number of discontinuities of the first kind, of the Cauchy problem with the initial condition being a continuous and piecewise differentiable function is proven.