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Your name. Close Send. In this article, the existence of a very weak solution for differential-operator equations of second order with nonlinear operator in the main part is proved. We would like to note that, in particular, if A is the differential operator this equation becomes a hyperbolic equation. Consequently, one can investigate previously not studied nonlinear hyperbolic equations with the use of results and the approach presented in this article.
The following work will be focused on nonlinear hyperbolic equations with the nonlinearity of the same type as studied here.
Moreover, here the long-time behavior of the very weak solution of the problem is proved, and also the dependence of the behavior of the solution from initial datums is shown. Bressan A. Cao D. Nonlinear dynamics of elastic rods using the Cosserat theory: Modelling and simulation. Solids Struct. Herty M. Coupling conditions for a class of second-order models for traffic flow. SIAM J. Evans L. Levine H. Lions J-L. Quelques methodes de resolution des problemes aux limites non lineaires , Paris : Dunod, , xx, p. Soltanov K. Some nonlinear equations of the nonstable filtration type and embedding theorems.
Nonlinear Analysis: T. Zeidler E. Bennett C. Some applications of nonlinearanalysis to di erential equations , ELM, Baku, , p. We would like to note that this equation shows the stability of the energy of the considered system in this case. Export Citation.
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Soltanov Corresponding author Institute Math. Abstract Here we study the existence of a solution and also the behavior of the existing solution of the abstract nonlinear differential equation of second order that, in particular, is the nonlinear hyperbolic equation with nonlinear main parts, and in the special case, is the equation of the type of equation of traffic flow.