On solution of pseudohyperbolic equation with constant coefficients

• Yury Kostikov Moscow Aviation Institute (National Research University) Volokolamskoe shosse, Moscow, Rusia.
• Aleksandr Romanenkov Russian Academy of Sciences Vavilova, Moscow, Rusia. https://orcid.org/0000-0002-0700-8465

DOI: https://doi.org/10.46925//rdluz.39.12

Keywords: Pseudohyperbolic equation, exact problem-solving solutions, solution properties

Abstract

The paper proposes the method of forming the exact solution of the first initial boundary value problem for one-dimensional linear pseudohyperbolic equation with constant coefficients. To obtain the solution type, the modification of partition method (Fourier method) is used, when the type of one of the solution functional factors is considered to be known. At the same time, the initial problem is reduced to parameterized family of Cauchy problems for ordinary differential equations. The paper presents explicitly calculated formulas, which specify the solution. The qualitative research of the solution properties has been conducted. The conditions for coefficients in the form of inequalities have been obtained that is indicative of boundedness and variability of the solutions. Several examples confirming the results obtained have been considered.

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