Open AccessClassical solutions for a class of nonlinear wave equations
Author(s) -
Svetlin G. Georgiev,
Karima Mebarki,
Khaled Zennir
Publication year - 2021
Publication title -
theoretical and applied mechanics/theoretical and applied mechanics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.279
H-Index - 6
eISSN - 2406-0925
pISSN - 1450-5584
DOI - 10.2298/tam201123013g
Subject(s) - nonlinear system , mathematics , class (philosophy) , representation (politics) , partial differential equation , initial value problem , mathematical analysis , hyperbolic partial differential equation , type (biology) , physics , computer science , quantum mechanics , artificial intelligence , politics , political science , law , biology , ecology
We study a class of initial value problems subject to nonlinear partial differential equations of hyperbolic type. A new topological approach is applied to prove the existence of nontrivial nonnegative solutions. More precisely, we propose a new integral representation of the solutions for the considered initial value problems and using this integral representation we establish existence of classical solutions for the considered classes of nonlinear wave equations.