Symmetry Analysis and Conservation Laws of a Generalization of the Kelvin-Voigt Viscoelasticity Equation

Abstract

In this paper, we study a generalization of the well-known Kelvin-Voigt viscoelasticity equation describing the mechanical behaviour of viscoelasticity. We perform a Lie symmetry analysis. Hence, we obtain the Lie point symmetries of the equation, allowing us to transform the partial differential equation into an ordinary differential equation by using the symmetry reductions. Furthermore, we determine the conservation laws of this equation by applying the multiplier method.

Lie groups and continuum mechanics: where do we stand today?

“…. [59][60][61][62][63][64][65][66][67][68]. In fluid mechanics, self-similar solutions of the Navier-Stokes equations have been computed [69][70][71][72] some decades ago.…”

Conserved quantities, optimal system and explicit solutions of a (1 + 1)-dimensional generalised coupled mKdV-type system

“…Nonlinear partial differential equations (NLPDEs) have rapidly become indispensable in the quest to conceptualise the world around us [1] , [2] , [3] , [4] , [5] , [6] , [7] , [8] , [9] , [10] , [11] , [12] , [13] , [14] , [15] , [16] , [17] , [18] , [19] , [20] , [21] , [22] , [23] , [24] , [25] , [26] , [27] , [28] , [29] , [30] , [31] , [32] , [33] , [34] , [35] , [36] , [37] , [38] , [39] , [40] , [41] , [42] , [43] , [44] , [45] , [46] , [47] , [48] , [49] , [50] . We give a few recent studies of NLPDEs presented in the literature.…”

“…A new method was introduced in [10] to find exact solutions for NLPDEs of mathematical physics. Symmetry analysis of the Kelvin-Voigt viscoelasticity equation and a generalized (2 + 1)-dimensional double dispersion equation was discussed in [11] , [12] .…”