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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, 15, De Gruyter, 2011. doi: 10.1515/9783110255294. 
[2] 
G. V. Demidenko and S. V. Uspenskii, Partial Differential Equations and Systems Not Solvable with Respect to the Highest Order Derivative, N.Y., Basel, Hong Kong, Marcel Dekker, Inc., 2003. doi: 10.1201/9780203911433. 
[3] 
A. Favini and A. Yagi, Degenerate Differential Equations in Banach Spaces, N.Y., Basel, Hong Kong, Marcel Dekker, Inc., 1999. 
[4] 
Yu. E. Gliklikh, Global and Stochastic Analysis with Applications to Mathematical Physics, London, Dordrecht, Heidelberg, N.Y., Springer, 2011. doi: 10.1007/9780857291639. 
[5] 
Yu. E. Gliklikh and E. Yu. Mashkov, Stochastic Leontieff type equations and mean derivatives of stochastic processes, Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming and Computer Software, 6 (2013), 2539. 
[6] 
M. Kovács and S. Larsson, Introduction to stochastic partial differential equations, in Proceedings of "New Directions in the Mathematical and Computer Sciences", National Universities Commission, Abuja, Nigeria, October 812, 2007 Publications of the ICMCS, 4 (2008), 159232. 
[7] 
A. I. Kozhanov, Boundary Problems for Odd Ordered Equations of Mathematical Physics, Novosibirsk, NGU, 1990. 
[8] 
L. D. Landau and E. M. Lifshits, Theoretical Phisics, VII. Elasticity Theory, Mscow, Nauka, 1987. 
[9] 
I. V. Melnikova, A. I. Filinkov and M. A. Alshansky, Abstract stochastic equations II. Solutions in spaces of abstract stochastic distributions, Journal of Mathematical Sciences, 116 (2003), 36203656. doi: 10.1023/A:1024159908410. 
[10] 
A. L. Shestakov, A. V. Keller and E. I. Nazarova, Numerical solution of the optimal measurement problem, Automation and Remote Control, 73 (2012), 97104. doi: 10.1134/S0005117912010079. 
[11] 
A. L. Shestakov and G. A. Sviridyuk, On a new conception of white noise, Obozrenie Prikladnoy i Promyshlennoy Matematiki, 19 (2012), 287288. 
[12] 
A. L. Shestakov and G. A. Sviridyuk, On the measurement of the "white noise", Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming and Computer Software, 286 (2012), 99108. 
[13] 
A. L. Shestakov and G. A. Sviridyuk, Optimal measurement of dynamically distorted signals, Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming and Computer Software, 234 (2011), 7075. 
[14] 
A. L. Shestakov, G. A. Sviridyuk and Yu. V. Hudyakov, Dynamic measurement in spaces of "noise", Bulletin of the South Ural State University. Series: Computer Technologies, Automatic Control and Radioelectronics, 13 (2013), 411. 
[15] 
R. E. Showalter, Hilbert Space Methods for Partial Differential Equations, Pitman, London, San Francisco, Melbourne, 1977. 
[16] 
N. Sidorov, B. Loginov, A. Sinithyn and M. Falaleev, LyapunovShmidt Methods in Nonlinear Analysis and Applications, Dordrecht, Boston, London, Kluwer Academic Publishers, 2002. doi: 10.1007/9789401721226. 
[17] 
G. A. Sviridyuk and T. V. Apetova, The phase spaces of linear dynamic Sobolev type equations, Doklady Akademii Nauk, 330 (1993), 696699. 
[18] 
G. A. Sviridyuk and V. E. Fedorov, Linear Sobolev Type Equations and Degenerate Semigroups of Operators, Utrecht, Boston, Köln, Tokyo, VSP, 2003. doi: 10.1515/9783110915501. 
[19] 
G. A. Sviridyuk and N. A. Manakova, The Dynamical Models of Sobolev Type with Showalter  Sidorov Condition and Additive 'Noise', Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming and Computer Software, 7 (2014), 90103. 
[20] 
G. A. Sviridyuk and O. V. Vakarina, Linear Sobolev type equations of higher order, Doklady Akademii Nauk, 393 (1998), 308310. 
[21] 
G. A. Sviridyuk and A. A. Zamyshlyaeva, The phase spaces of a class of linear higherorder Sobolev type equations, Differential Equations, 42 (2006), 269278. doi: 10.1134/S0012266106020145. 
[22]  
[23] 
S. Wang and G. Chen, Small amplitude solutions of the generalized IMBq equation, Mathematical Analysis and Applications, 274 (2002), 846866. doi: 10.1016/S0022247X(02)004018. 
[24] 
S. A. Zagrebina and E. A. Soldatova, The linear Sobolevtype equations with relatively pbounded operators and additive white noise, The Bulletin of Irkutsk State University. Series "Mathematics", 6 (2013), 2034. 
[25] 
A. A. Zamyshlyaeva, The higherorder Sobolevtype models, Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming and Computer Software, 7 (2014), 528. 
[26] 
A. A. Zamyshlyaeva, Stochastic incomplete linear Sobolev type highordered equations with additive white noise, Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming and Computer Software, 299 (2012), 7382. 
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, 15, De Gruyter, 2011. doi: 10.1515/9783110255294. 
[2] 
G. V. Demidenko and S. V. Uspenskii, Partial Differential Equations and Systems Not Solvable with Respect to the Highest Order Derivative, N.Y., Basel, Hong Kong, Marcel Dekker, Inc., 2003. doi: 10.1201/9780203911433. 
[3] 
A. Favini and A. Yagi, Degenerate Differential Equations in Banach Spaces, N.Y., Basel, Hong Kong, Marcel Dekker, Inc., 1999. 
[4] 
Yu. E. Gliklikh, Global and Stochastic Analysis with Applications to Mathematical Physics, London, Dordrecht, Heidelberg, N.Y., Springer, 2011. doi: 10.1007/9780857291639. 
[5] 
Yu. E. Gliklikh and E. Yu. Mashkov, Stochastic Leontieff type equations and mean derivatives of stochastic processes, Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming and Computer Software, 6 (2013), 2539. 
[6] 
M. Kovács and S. Larsson, Introduction to stochastic partial differential equations, in Proceedings of "New Directions in the Mathematical and Computer Sciences", National Universities Commission, Abuja, Nigeria, October 812, 2007 Publications of the ICMCS, 4 (2008), 159232. 
[7] 
A. I. Kozhanov, Boundary Problems for Odd Ordered Equations of Mathematical Physics, Novosibirsk, NGU, 1990. 
[8] 
L. D. Landau and E. M. Lifshits, Theoretical Phisics, VII. Elasticity Theory, Mscow, Nauka, 1987. 
[9] 
I. V. Melnikova, A. I. Filinkov and M. A. Alshansky, Abstract stochastic equations II. Solutions in spaces of abstract stochastic distributions, Journal of Mathematical Sciences, 116 (2003), 36203656. doi: 10.1023/A:1024159908410. 
[10] 
A. L. Shestakov, A. V. Keller and E. I. Nazarova, Numerical solution of the optimal measurement problem, Automation and Remote Control, 73 (2012), 97104. doi: 10.1134/S0005117912010079. 
[11] 
A. L. Shestakov and G. A. Sviridyuk, On a new conception of white noise, Obozrenie Prikladnoy i Promyshlennoy Matematiki, 19 (2012), 287288. 
[12] 
A. L. Shestakov and G. A. Sviridyuk, On the measurement of the "white noise", Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming and Computer Software, 286 (2012), 99108. 
[13] 
A. L. Shestakov and G. A. Sviridyuk, Optimal measurement of dynamically distorted signals, Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming and Computer Software, 234 (2011), 7075. 
[14] 
A. L. Shestakov, G. A. Sviridyuk and Yu. V. Hudyakov, Dynamic measurement in spaces of "noise", Bulletin of the South Ural State University. Series: Computer Technologies, Automatic Control and Radioelectronics, 13 (2013), 411. 
[15] 
R. E. Showalter, Hilbert Space Methods for Partial Differential Equations, Pitman, London, San Francisco, Melbourne, 1977. 
[16] 
N. Sidorov, B. Loginov, A. Sinithyn and M. Falaleev, LyapunovShmidt Methods in Nonlinear Analysis and Applications, Dordrecht, Boston, London, Kluwer Academic Publishers, 2002. doi: 10.1007/9789401721226. 
[17] 
G. A. Sviridyuk and T. V. Apetova, The phase spaces of linear dynamic Sobolev type equations, Doklady Akademii Nauk, 330 (1993), 696699. 
[18] 
G. A. Sviridyuk and V. E. Fedorov, Linear Sobolev Type Equations and Degenerate Semigroups of Operators, Utrecht, Boston, Köln, Tokyo, VSP, 2003. doi: 10.1515/9783110915501. 
[19] 
G. A. Sviridyuk and N. A. Manakova, The Dynamical Models of Sobolev Type with Showalter  Sidorov Condition and Additive 'Noise', Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming and Computer Software, 7 (2014), 90103. 
[20] 
G. A. Sviridyuk and O. V. Vakarina, Linear Sobolev type equations of higher order, Doklady Akademii Nauk, 393 (1998), 308310. 
[21] 
G. A. Sviridyuk and A. A. Zamyshlyaeva, The phase spaces of a class of linear higherorder Sobolev type equations, Differential Equations, 42 (2006), 269278. doi: 10.1134/S0012266106020145. 
[22]  
[23] 
S. Wang and G. Chen, Small amplitude solutions of the generalized IMBq equation, Mathematical Analysis and Applications, 274 (2002), 846866. doi: 10.1016/S0022247X(02)004018. 
[24] 
S. A. Zagrebina and E. A. Soldatova, The linear Sobolevtype equations with relatively pbounded operators and additive white noise, The Bulletin of Irkutsk State University. Series "Mathematics", 6 (2013), 2034. 
[25] 
A. A. Zamyshlyaeva, The higherorder Sobolevtype models, Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming and Computer Software, 7 (2014), 528. 
[26] 
A. A. Zamyshlyaeva, Stochastic incomplete linear Sobolev type highordered equations with additive white noise, Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming and Computer Software, 299 (2012), 7382. 
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