This article is cited in 3 papers

Differentical equations, dynamical systems and optimal control

Linear problem of shock wave disturbance analysis. Part 1: General solution, incidence, refraction and reflection in general case

E. V. Semenko

Novosibirsk State Pedagogical University, Viluiskaya Street 28, 630126, Novosibirsk, Russia

Abstract: This article is devoted to the linear problem of shock wave disturbance, where a number of questions related to this problem are considered. A new representation of problem's solution, having completely algebraic form in spectral variables, is found, which allows us to scrutinize the problem, obtain new results and refine known ones. The analytical results are approved and illustrated by numerical calculations.
A whole article is divided into three parts because of a large volume.
In first part, the basic representation of initial-value problem's solution is established, and the basic techniques of its analysis — singular and regular terms detachment, incident, refracted and reflected waves separation — is described. On this basic, the incidence upon the shock, refraction and reflection of waves in general form is inspected.
The peculiarity of refraction, which haven't been noted before, is found: any incident wave may be decomposed into the sum of waves with physically different interaction with shock, namely, one summand interacts with shock, i.e. generates shock disturbance, but doesn't generate any transmitted waves; other summands don't interact with shock, i.e. don't generate shock disturbance, but generate different kinds of transmitted waves.
A post-shock incidence of different kinds of waves and its reflection is inspected, in particular a four-wave configuration at reflection is stated.

Keywords: shock wave, shock disturbance, entropy-vorticity wave, acoustic wave, incident wave, refraction, transmitted wave, reflection, reflected wave, stability, neutral stability, spontaneous emission, Fourier transform.

UDC: 517.958, 532.5

MSC: 35A21, 35A22, 35D30, 76L05

Received December 13, 2016, published May 23, 2017

Language: English

DOI: 10.17377/semi.2017.14.038

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