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Global existence and dynamic structure of solutions for damped wave equation involving the fractional Laplacian

Bidi Younes, Beniani Abderrahmane, Zennir Khaled, Himadan Ahmed

Demonstratio Mathematica

2021

Vol. 54, nr 1

245--258

We consider strong damped wave equation involving the fractional Laplacian with nonlinear source. The results of global solution under necessary conditions on the critical exponent are established. The existence is proved by using the Galerkin approximations combined with the potential well theory. Moreover, we showed new decay estimates of global solution.

On some nonlinear hyperbolic p(x,t)-Laplacian equations

Ahmedatt T., Touzani A., Aberqi A., Yazough C.

Journal of Applied Analysis

2018

Vol. 24, nr 1

55--69

This paper is devoted to study the global existence of solutions of the hyperbolic Dirichlet equation Utt=Lu+f(x,t) in ΩT=Ω×(0,T), where L is a nonlinear operator and ϕ(x,t,⋅), f(x,t) and the exponents of the nonlinearities p(x,t) and μ(x,t) are given functions.

The nonlocal Darboux problem on the unbounded region in Banach spaces

Majcher P.

Demonstratio Mathematica

2008

Vol. 41, nr 2

389-402

In this paper we study existence theorems of solutions for the hyperbolic Darboux problem of the form [..] with nonlocal boundary conditions u(x, 0) +h1(u) = g1(x),u(0,y) +h2(u)= g2(y), on the unbounded region. The functions defining nonlocal conditions satisfy the Lipschitz condition with respect to a measure of noncompactness.

On the modelling of hyperbolic heat conduction problems in periodic lattice structures

Szymczyk J., Woźniak C.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

2003

Vol. 2, nr 1

183--189

A new modelling approach to the hyperbolic heat conduction problems in periodic lattice structures of an arbitrary form is discussed. Taking into account the results obtained in [5] we introduce a special description of the periodic lattice geometry which leads to the heat conduction model governed by the system of finite difference equations. The continuum models are derived from the finite difference equations by using the principle of stationary action.