Geodesic
Solution of a problem for a system of third order partial differential equations
Vestnik rossijskih universitetov. Matematika, Tome 26 (2021) no. 133, pp. 68-76

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An initial-boundary value problem for a system of third-order partial differential equations is considered. Equations and systems of equations with the highest mixed third derivative describe heat exchange in the soil complicated by the movement of soil moisture, quasi-stationary processes in a two-component semiconductor plasma, etc. The system is reduced to a differential equation with a degenerate operator at the highest derivative with respect to the distinguished variable in a Banach space. This operator has the property of having 0 as a normal eigenvalue, which makes it possible to split the original equations into an equation in subspaces. The conditions are obtained under which a unique solution to the problem exists; the analytical formula is found.
Keywords: initial-boundary value problem; system of third order partial differential equations; mixed derivative; 0 as normal eigenvalue; differential equation in Banach space; solution. 
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     author = {V. I. Uskov},
     title = {Solution of a problem for a system of third order partial differential equations},
     journal = {Vestnik rossijskih universitetov. Matematika},
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     year = {2021},
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     url = {http://geodesic.mathdoc.fr/item/VTAMU_2021_26_133_a6/}
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V. I. Uskov. Solution of a problem for a system of third order partial differential equations. Vestnik rossijskih universitetov. Matematika, Tome 26 (2021) no. 133, pp. 68-76. http://geodesic.mathdoc.fr/item/VTAMU_2021_26_133_a6/