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One Class of Sobolev Type Equations of Higher Order with Additive "White Noise"
1.  University of Bologna, Department of Mathematics, Piazza di Porta San Donato, 5, Bologna, Italy 
2.  South Ural State University, Dep. of Mathematics, Mechanics and Computer science, Lenin avenue, 76, Chelyabinsk, Russian Federation, Russian Federation 
References:
[1] 
A. B. Al'shin, M. O. Korpusov and A. G. Sveshnikov, Blowup in Nonlinear Sobolev Type Equations,, Series in Nonlinear Analysis and Applications, (2011). doi: 10.1515/9783110255294. Google Scholar 
[2] 
G. V. Demidenko and S. V. Uspenskii, Partial Differential Equations and Systems Not Solvable with Respect to the Highest Order Derivative,, N.Y., (2003). doi: 10.1201/9780203911433. Google Scholar 
[3] 
A. Favini and A. Yagi, Degenerate Differential Equations in Banach Spaces,, N.Y., (1999). Google Scholar 
[4] 
Yu. E. Gliklikh, Global and Stochastic Analysis with Applications to Mathematical Physics,, London, (2011). doi: 10.1007/9780857291639. Google Scholar 
[5] 
Yu. E. Gliklikh and E. Yu. Mashkov, Stochastic Leontieff type equations and mean derivatives of stochastic processes,, \emph{Bulletin of the South Ural State University. Series: Mathematical Modelling, 6 (2013), 25. Google Scholar 
[6] 
M. Kovács and S. Larsson, Introduction to stochastic partial differential equations,, in \emph{Proceedings of, 4 (2008), 8. Google Scholar 
[7] 
A. I. Kozhanov, Boundary Problems for Odd Ordered Equations of Mathematical Physics,, Novosibirsk, (1990). Google Scholar 
[8] 
L. D. Landau and E. M. Lifshits, Theoretical Phisics, VII. Elasticity Theory,, Mscow, (1987). Google Scholar 
[9] 
I. V. Melnikova, A. I. Filinkov and M. A. Alshansky, Abstract stochastic equations II. Solutions in spaces of abstract stochastic distributions,, \emph{Journal of Mathematical Sciences}, 116 (2003), 3620. doi: 10.1023/A:1024159908410. Google Scholar 
[10] 
A. L. Shestakov, A. V. Keller and E. I. Nazarova, Numerical solution of the optimal measurement problem,, \emph{Automation and Remote Control}, 73 (2012), 97. doi: 10.1134/S0005117912010079. Google Scholar 
[11] 
A. L. Shestakov and G. A. Sviridyuk, On a new conception of white noise,, \emph{Obozrenie Prikladnoy i Promyshlennoy Matematiki}, 19 (2012), 287. Google Scholar 
[12] 
A. L. Shestakov and G. A. Sviridyuk, On the measurement of the "white noise",, \emph{Bulletin of the South Ural State University. Series: Mathematical Modelling, 286 (2012), 99. Google Scholar 
[13] 
A. L. Shestakov and G. A. Sviridyuk, Optimal measurement of dynamically distorted signals,, \emph{Bulletin of the South Ural State University. Series: Mathematical Modelling, 234 (2011), 70. Google Scholar 
[14] 
A. L. Shestakov, G. A. Sviridyuk and Yu. V. Hudyakov, Dynamic measurement in spaces of "noise",, \emph{Bulletin of the South Ural State University. Series: Computer Technologies, 13 (2013), 4. Google Scholar 
[15] 
R. E. Showalter, Hilbert Space Methods for Partial Differential Equations,, Pitman, (1977). Google Scholar 
[16] 
N. Sidorov, B. Loginov, A. Sinithyn and M. Falaleev, LyapunovShmidt Methods in Nonlinear Analysis and Applications,, Dordrecht, (2002). doi: 10.1007/9789401721226. Google Scholar 
[17] 
G. A. Sviridyuk and T. V. Apetova, The phase spaces of linear dynamic Sobolev type equations,, \emph{Doklady Akademii Nauk}, 330 (1993), 696. Google Scholar 
[18] 
G. A. Sviridyuk and V. E. Fedorov, Linear Sobolev Type Equations and Degenerate Semigroups of Operators,, Utrecht, (2003). doi: 10.1515/9783110915501. Google Scholar 
[19] 
G. A. Sviridyuk and N. A. Manakova, The Dynamical Models of Sobolev Type with Showalter  Sidorov Condition and Additive 'Noise',, \emph{Bulletin of the South Ural State University. Series: Mathematical Modelling, 7 (2014), 90. Google Scholar 
[20] 
G. A. Sviridyuk and O. V. Vakarina, Linear Sobolev type equations of higher order,, \emph{Doklady Akademii Nauk}, 393 (1998), 308. Google Scholar 
[21] 
G. A. Sviridyuk and A. A. Zamyshlyaeva, The phase spaces of a class of linear higherorder Sobolev type equations,, \emph{Differential Equations}, 42 (2006), 269. doi: 10.1134/S0012266106020145. Google Scholar 
[22] 
G. Uizem, Linear and Nonlinear Waves,, Mscow, (1977). Google Scholar 
[23] 
S. Wang and G. Chen, Small amplitude solutions of the generalized IMBq equation,, \emph{Mathematical Analysis and Applications}, 274 (2002), 846. doi: 10.1016/S0022247X(02)004018. Google Scholar 
[24] 
S. A. Zagrebina and E. A. Soldatova, The linear Sobolevtype equations with relatively pbounded operators and additive white noise,, \emph{The Bulletin of Irkutsk State University. Series, 6 (2013), 20. Google Scholar 
[25] 
A. A. Zamyshlyaeva, The higherorder Sobolevtype models,, \emph{Bulletin of the South Ural State University. Series: Mathematical Modelling, 7 (2014), 5. Google Scholar 
[26] 
A. A. Zamyshlyaeva, Stochastic incomplete linear Sobolev type highordered equations with additive white noise,, \emph{Bulletin of the South Ural State University. Series: Mathematical Modelling, 299 (2012), 73. Google Scholar 
show all references
References:
[1] 
A. B. Al'shin, M. O. Korpusov and A. G. Sveshnikov, Blowup in Nonlinear Sobolev Type Equations,, Series in Nonlinear Analysis and Applications, (2011). doi: 10.1515/9783110255294. Google Scholar 
[2] 
G. V. Demidenko and S. V. Uspenskii, Partial Differential Equations and Systems Not Solvable with Respect to the Highest Order Derivative,, N.Y., (2003). doi: 10.1201/9780203911433. Google Scholar 
[3] 
A. Favini and A. Yagi, Degenerate Differential Equations in Banach Spaces,, N.Y., (1999). Google Scholar 
[4] 
Yu. E. Gliklikh, Global and Stochastic Analysis with Applications to Mathematical Physics,, London, (2011). doi: 10.1007/9780857291639. Google Scholar 
[5] 
Yu. E. Gliklikh and E. Yu. Mashkov, Stochastic Leontieff type equations and mean derivatives of stochastic processes,, \emph{Bulletin of the South Ural State University. Series: Mathematical Modelling, 6 (2013), 25. Google Scholar 
[6] 
M. Kovács and S. Larsson, Introduction to stochastic partial differential equations,, in \emph{Proceedings of, 4 (2008), 8. Google Scholar 
[7] 
A. I. Kozhanov, Boundary Problems for Odd Ordered Equations of Mathematical Physics,, Novosibirsk, (1990). Google Scholar 
[8] 
L. D. Landau and E. M. Lifshits, Theoretical Phisics, VII. Elasticity Theory,, Mscow, (1987). Google Scholar 
[9] 
I. V. Melnikova, A. I. Filinkov and M. A. Alshansky, Abstract stochastic equations II. Solutions in spaces of abstract stochastic distributions,, \emph{Journal of Mathematical Sciences}, 116 (2003), 3620. doi: 10.1023/A:1024159908410. Google Scholar 
[10] 
A. L. Shestakov, A. V. Keller and E. I. Nazarova, Numerical solution of the optimal measurement problem,, \emph{Automation and Remote Control}, 73 (2012), 97. doi: 10.1134/S0005117912010079. Google Scholar 
[11] 
A. L. Shestakov and G. A. Sviridyuk, On a new conception of white noise,, \emph{Obozrenie Prikladnoy i Promyshlennoy Matematiki}, 19 (2012), 287. Google Scholar 
[12] 
A. L. Shestakov and G. A. Sviridyuk, On the measurement of the "white noise",, \emph{Bulletin of the South Ural State University. Series: Mathematical Modelling, 286 (2012), 99. Google Scholar 
[13] 
A. L. Shestakov and G. A. Sviridyuk, Optimal measurement of dynamically distorted signals,, \emph{Bulletin of the South Ural State University. Series: Mathematical Modelling, 234 (2011), 70. Google Scholar 
[14] 
A. L. Shestakov, G. A. Sviridyuk and Yu. V. Hudyakov, Dynamic measurement in spaces of "noise",, \emph{Bulletin of the South Ural State University. Series: Computer Technologies, 13 (2013), 4. Google Scholar 
[15] 
R. E. Showalter, Hilbert Space Methods for Partial Differential Equations,, Pitman, (1977). Google Scholar 
[16] 
N. Sidorov, B. Loginov, A. Sinithyn and M. Falaleev, LyapunovShmidt Methods in Nonlinear Analysis and Applications,, Dordrecht, (2002). doi: 10.1007/9789401721226. Google Scholar 
[17] 
G. A. Sviridyuk and T. V. Apetova, The phase spaces of linear dynamic Sobolev type equations,, \emph{Doklady Akademii Nauk}, 330 (1993), 696. Google Scholar 
[18] 
G. A. Sviridyuk and V. E. Fedorov, Linear Sobolev Type Equations and Degenerate Semigroups of Operators,, Utrecht, (2003). doi: 10.1515/9783110915501. Google Scholar 
[19] 
G. A. Sviridyuk and N. A. Manakova, The Dynamical Models of Sobolev Type with Showalter  Sidorov Condition and Additive 'Noise',, \emph{Bulletin of the South Ural State University. Series: Mathematical Modelling, 7 (2014), 90. Google Scholar 
[20] 
G. A. Sviridyuk and O. V. Vakarina, Linear Sobolev type equations of higher order,, \emph{Doklady Akademii Nauk}, 393 (1998), 308. Google Scholar 
[21] 
G. A. Sviridyuk and A. A. Zamyshlyaeva, The phase spaces of a class of linear higherorder Sobolev type equations,, \emph{Differential Equations}, 42 (2006), 269. doi: 10.1134/S0012266106020145. Google Scholar 
[22] 
G. Uizem, Linear and Nonlinear Waves,, Mscow, (1977). Google Scholar 
[23] 
S. Wang and G. Chen, Small amplitude solutions of the generalized IMBq equation,, \emph{Mathematical Analysis and Applications}, 274 (2002), 846. doi: 10.1016/S0022247X(02)004018. Google Scholar 
[24] 
S. A. Zagrebina and E. A. Soldatova, The linear Sobolevtype equations with relatively pbounded operators and additive white noise,, \emph{The Bulletin of Irkutsk State University. Series, 6 (2013), 20. Google Scholar 
[25] 
A. A. Zamyshlyaeva, The higherorder Sobolevtype models,, \emph{Bulletin of the South Ural State University. Series: Mathematical Modelling, 7 (2014), 5. Google Scholar 
[26] 
A. A. Zamyshlyaeva, Stochastic incomplete linear Sobolev type highordered equations with additive white noise,, \emph{Bulletin of the South Ural State University. Series: Mathematical Modelling, 299 (2012), 73. Google Scholar 
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