Geodesic
Symmetry analysis of nonlinear pseudoparabolic equation
Čelâbinskij fiziko-matematičeskij žurnal, Tome 2 (2017) no. 2, pp. 152-168

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The group classification is obtained for quasilinear pseudoparabolic equation with a free element depending on the first order time derivative. Four-dimensional kernel of principal groups and all free element specifications up to equivalence transformations which correspond to additional symmetries of the equation are found. For some nonlinear specifications optimal one-dimensional subalgebras system of five-dimensional principal Lie algebra and corresponding invariant solutions or invariant submodels are calculated. Besides, nonlinear self-adjointness is shown for the operator that defining the linear equation of the species. A series of conservation laws of a linear equation was searched.
Keywords: pseudoparabolic equation, group analysis, group classification, invariant solution, conservation law. 
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     author = {E. A. Bezbogova and V. E. Fedorov and A. S. Avilovich},
     title = {Symmetry analysis of  nonlinear pseudoparabolic equation},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
     pages = {152--168},
     publisher = {mathdoc},
     volume = {2},
     number = {2},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2017_2_2_a1/}
}
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E. A. Bezbogova; V. E. Fedorov; A. S. Avilovich. Symmetry analysis of  nonlinear pseudoparabolic equation. Čelâbinskij fiziko-matematičeskij žurnal, Tome 2 (2017) no. 2, pp. 152-168. http://geodesic.mathdoc.fr/item/CHFMJ_2017_2_2_a1/