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On the symmetries and conservation laws of the multidimensional nonlinear damped wave equations. (English) Zbl 1400.35012

Summary: We carry out a classification of Lie symmetries for the (\(2 + 1\))-dimensional nonlinear damped wave equation \(u_{t t} + f \left(u\right) u_t = \mathrm{div}(g \left(u\right) \mathrm{grad} u)\) with variable damping. Similarity reductions of the equation are performed using the admitted Lie symmetries of the equation and some interesting solutions are presented. Employing the multiplier approach, admitted conservation laws of the equation are constructed for some new, interesting cases.

MSC:

35B06 Symmetries, invariants, etc. in context of PDEs
35L71 Second-order semilinear hyperbolic equations
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