The phase spaces of a class of linear higher-order Sobolev type equations

2006 ◽  
Vol 42 (2) ◽  
pp. 269-278 ◽  
Author(s):  
G. A. Sviridyuk ◽  
A. A. Zamyshlyaeva
Keyword(s):  
Higher Order ◽  
Sobolev Type

One Class of Sobolev Type Equations of Higher Order with Additive "White Noise"

2015 ◽  
Vol 15 (1) ◽  
pp. 185-196 ◽  
Author(s):  
Alyona A. Zamyshlyaeva ◽  
Georgy A. Sviridyuk ◽  
Angelo Favini
Keyword(s):  
White Noise ◽  
Higher Order ◽  
Sobolev Type ◽  
Additive White Noise

Incomplete Sobolev type equations of higher order with "white noise" in quasi-Banach spaces

2016 ◽  
Vol 10 ◽  
pp. 1811-1819
Author(s):  
Alyona A. Zamyshlyaeva ◽  
Evgeniy V. Bychkov ◽  
Olga N. Tsyplenkova
Keyword(s):  
White Noise ◽  
Banach Spaces ◽  
Higher Order ◽  
Sobolev Type

scholarly journals Inverse Problem for the Sobolev Type Equation of Higher Order

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1647
Author(s):  
Alyona Zamyshlyaeva ◽  
Aleksandr Lut
Keyword(s):  
Inverse Problem ◽  
Bounded Operator ◽  
Type Equation ◽  
Higher Order ◽  
Successive Approximations ◽  
Unknown Coefficient ◽  
Method Of Successive Approximations ◽  
Sobolev Type ◽  
Equivalent Problems ◽  
Sobolev Type Equation

The article investigates the inverse problem for a complete, inhomogeneous, higher-order Sobolev type equation, together with the Cauchy and overdetermination conditions. This problem was reduced to two equivalent problems in the aggregate: regular and singular. For these problems, the theory of polynomially bounded operator pencils is used. The unknown coefficient of the original equation is restored using the method of successive approximations. The main result of this work is a theorem on the unique solvability of the original problem. This study continues and generalizes the authors’ previous research in this area. All the obtained results can be applied to the mathematical modeling of various processes and phenomena that fit the problem under study.

scholarly journals Travelling Wave Solutions to the Benney-Luke and the Higher-Order Improved Boussinesq Equations of Sobolev Type

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Ömer Faruk Gözükızıl ◽  
Şamil Akçağıl
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Boussinesq Equation ◽  
Boussinesq Equations ◽  
Travelling Wave ◽  
Higher Order ◽  
Sobolev Type ◽  
Travelling Wave Solutions ◽  
Partial Differential ◽  
Wave Solutions

By using the tanh-coth method, we obtained some travelling wave solutions of two well-known nonlinear Sobolev type partial differential equations, namely, the Benney-Luke equation and the higher-order improved Boussinesq equation. We show that the tanh-coth method is a useful, reliable, and concise method to solve these types of equations.

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