Heaviside generalized functions and shock waves for a Burger kind equation
Francisco Villarreal
Abstract
Francisco Villarreal
Abstract
The purpose of the work is to study the existence and nonexistence of shock wave solutions for the Burger equations. The study is developed in the context of Colombeau's theory of generalized functions (GFs). This study uses the equality in the strict sense and the weak equality of GFs. The shock wave solutions are given in terms of GFs that have the Heaviside function, in x and (x, t) variables, as macroscopic aspect. This means that solutions are sought in the form of sequences of regularizations to the Heaviside function, in ℝ n and ℝ n ×ℝ, in the distributional limit sense.
OpenAlex reports 1 citations for this work. Citation counts describe recorded attention and do not establish research quality.
A contribution statement is not available in the OpenAlex record.
Method details are not available in the OpenAlex metadata.
Findings are not separately available in the OpenAlex metadata.
Limitations are not available in the OpenAlex metadata.
Application details are not available in the OpenAlex metadata.
The purpose of the work is to study the existence and nonexistence of shock wave solutions for the Burger equations. The study is developed in the context of Colombeau's theory of generalized functions (GFs). This study uses the equality in the strict sense and the weak equality of GFs. The shock wave solutions are given in terms of GFs that have the Heaviside function, in x and (x, t) variables, as macroscopic aspect. This means that solutions are sought in the form of sequences of regularizations to the Heaviside function, in ℝ n and ℝ n ×ℝ, in the distributional limit sense.
Key concepts: Heaviside step function, Mathematics, Generalized function, Context (archaeology), Shock wave, Mathematical analysis, Function (biology), Shock (circulatory)