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ORIGINAL RESEARCH article

Front. Appl. Math. Stat.
Sec. Mathematical Physics
Volume 10 - 2024 | doi: 10.3389/fams.2024.1467199
This article is part of the Research Topic Approximation Methods and Analytical Modeling Using Partial Differential Equations View all 19 articles

Qualitative analysis of fourth-order hyperbolic equations

Provisionally accepted
Yuliia Andreieva Yuliia Andreieva 1*Kateryna Buryachenko Kateryna Buryachenko 1,2
  • 1 Vasyl' Stus Donetsk National University, Vinnytsia, Ukraine
  • 2 Humboldt University of Berlin, Berlin, Baden-Wurttemberg, Germany

The final, formatted version of the article will be published soon.

    We investigate the qualitative properties of weak solutions to the boundary value problems for fourth-order linear hyperbolic equations with constant coefficients in a plane bounded domain convex with respect to characteristics. Our main scope is to prove some analogue of the maximum principle, solvability, uniqueness and regularity results for weak solutions of initial and boundary value problems in the space L^2.

    Keywords: Cauchy problem, Goursat problem, Dirichlet problem, Maximum Principle, hyperbolic fourth-order PDEs, Weak solutions, duality equation-domain, L-traces

    Received: 19 Jul 2024; Accepted: 15 Oct 2024.

    Copyright: © 2024 Andreieva and Buryachenko. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

    * Correspondence: Yuliia Andreieva, Vasyl' Stus Donetsk National University, Vinnytsia, Ukraine

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