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On a finding the coefficient of one nonlinear wave equation in the mixed problem

Safarova Zimrud R.

Archives of Control Sciences

2020

Vol. 30, No. 2

199--212

The paper is devoted to the finding of the coefficient of one nonlinear wave equation in the mixed problem. The considered problem is reduced to the optimal control problem with proper functional. Differentiability of functional is proved and the necessary optimality conditions are derived in the form of the variational inequality. Existence of the optimal control is proved.

Energy decay result for a nonlinear wave p-Laplace equation with a delay term

Zennir K., Laouar L. K.

Mathematica Applicanda

2017

Vol. 45, No. 1

65--80

We consider the nonlinear (in space and time) wave equation with delay term in the internal feedback. Under conditions on the delay term and the term without delay, we study the asymptotic behavior of solutions using the multiplier method and general weighted integral inequalities.

Rozważamy nieliniowe równanie falowe (w czasie i przestrzeni) z członem wewnętrznego sprzężenia zwrotnego. Przy pewnych warunkach na poszczególne człony równania badane jest asymptotyczne zachowanie rozwiązań.

A shock problem involving a nonlinear viscoelastic bar associated with a nonlinear boundary condition

Long N., Giai V., Truong L.

Demonstratio Mathematica

2008

Vol. 41, nr 1

85-108

We study the initial-boundary value problem for a nonlinear wave equation given by [...] where p > 2, q > l, K, lambda are given constants and uo, u1, F are given functions, the unknown function u(x,t) and the unknown boundary value P (t) satisfy the following nonlinear integral equation [...] where K1, alpha, beta are given constants and g, k arę given functions. In Part 1 we prove a theorem of existence and uniqueness of a weak solution (u, P) of problem (1), (2). The proof is based on the Faedo-Galerkin method associated with a priori estimates, weak convergence and compactness techniques. In Part 3 we obtain an asymptotic expansion of the solution (u, P) of the problem (1), (2) up to order N+1 in three small parameters K, lambda, K1.

On a nonlinear Kirchhoff-Carrier wave equation in the unit membrane: the quadratic convergence and asymptotic expansion of solutions

Long N., Ngoc L.

Demonstratio Mathematica

2007

Vol. 40, nr 2

365-392

In this paper we consider the initial-boundary value problem for the nonlinear wave equation.

Construction solutions of boundary problems for general nonlinear wave equation

Drohomiretska C.

Vibrations in Physical Systems

2000

Vol. 19

104--105