For a smooth linear second-order partial differential equation on the plane, a nonlocal canonical form of its principal symbol near the type change line is proposed, up to a smooth change of coordinates and multiplication by a non-vanishing smooth function. It is assumed that the discriminant of the characteristic equation and its differential do not vanish simultaneously, and that the field of characteristic directions is nowhere tangent to this line. This form can be used to construct solutions to model boundary value problems for such equations; in particular, it is applied to finding infinitesimal bendings of smooth surfaces close to surfaces of revolution, clamped along two curves near the type change line.
Keywords: mixed type equations, canonical form, principal symbol, small bendings of surfaces
Received April 08, 2026
Revised April 27, 2026
Accepted April 30, 2026
Aleksei A. Davydov, Dr. Phys.-Math. Sci., Prof., Corr. Member of the RAS, Lomonosov Moscow State University, Moscow, Russia, e-mail: davydov@mi-ras.ru
Yuliya A. Kasten, Senior Lecturer, Vladimir State University named after A.G. and N.G.Stoletovs, Vladimir, Russia, e-mail: julikasten@bk.ru
Anton S. Platov, Cand. Phys.-Math. Sci., Assoc. Prof., National University of Science and Technology MISIS, Moscow, Russia, e-mail: platovmm@mail.ru
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Cite this article as: A.A. Davydov, Yu.A. Kasten, A.S. Platov. Nonlocal canonical form of Tricomi–Cibrario near a smooth closed line of type change. Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2026, vol. 32, no. 2, pp. 87–99.
