INFORMATION PROCESSING IN STATE ANALYSIS FOR STOCHASTIC DYNAMIC AND EVOLUTIONARY SYSTEMS OF WENTZELL EQUATIONS

N. S. Goncharov

Abstract


The paper studies stochastic dynamical and evolutionary Wentzell systems in the domain and on its boundary.   In particular, a structural system analysis of various aspects of the study of Wentzell equation systems is carried out for the above Wentzell equation systems and an algorithm is constructed to process the information obtained from computational experiments and analyze the state of the stochastic dynamic and evolutionary Wentzell system at different values of their parameters.

Keywords


Wentzell's dynamical system; Wentzell's evolutionary system; Wentzell system of equations; information processing; three sigma rule; Nelson -- Glicklich derivative

Full Text:

PDF

References


Barenblatt G.I., ZheltovYu.P., Kochina I.N. The Basic Representations of the FiltrationTheory forHomogeneous Fluids inFissuredRocks. Journal of Applied MathematicsandMechanics, 1960, vol. 24, no. 5, pp.58–73. (in Russian)

Goncharov N.S., Zagrebina S.A., Sviridyuk G.A. Non-Uniqueness of Solutions to Boundary Value Problems with Wentzell Condition. Bulletin of the South Ural State University. Series: Mathematical Modeling, Programming and Computer Software, 2021, vol. 14, no. 4, pp. 102–105. DOI: 10.14529/mmp210408

Dzektser E.S. Generalization of the Equation of Motion of Ground Waters with Free Surface. Doklady Akademii Nauk SSSR, 1972, vol. 202, no. 5, pp. 1031–1033. (in Russian)

Wentzell A.D. Semigroups of Operators Corresponding to a Generalized Differential Operator of Second Order. Doklady Academii Nauk SSSR, 1956, vol. 111, pp. 269–272. (inRussian)

Apushkinskaya D.E., Nazarov A.I. An Initial Boundary Value Problem with a Venttsel’ Boundary Condition for Parabolic Equations not in Divergence Form. St. Petersburg Math. J., 1995, vol. 6, no. 6, pp. 1127–1149.

Apushkinskaya D.E., Nazarov A.I. Quasilinear Twophase Venttsel Problems. Journal of Mathematical Sciences, 2003, vol. 115, no. 6, pp. 2704–2719. DOI:10.1023/A:1023305432516

Lukyanov V.V., Nazarov A.I. Solving of Vent’sel Boundary value Problem for Laplace and Helmholtz Equations by Iterated Potentials. Journal of Mathematical Sciences, 2000, vol. 102, no. 4, pp. 4265–4274.

Apushkinskaya D.E., Nazarov A.I., Palagachev D.K., Softova L.G. Nonstationary Venttsel Problem with VMOx leading coefficients. Doklady Mathematics, 2023, vol. 107, no. 2, pp.97–100. DOI: 10.1134/S1064562423700679

Apushkinskaya D.E., Nazarov A.I., Palagachev D.K., Softova L.G. Lp Theory of Venttsel BVPS with Discontinuos Data. AAPP Atti della Accademia Peloritana dei Pericolanti Classe di Scienze Fisiche, Matematiche e Naturali, 2020, vol. 98, no. A1. DOI: 10.1137/19M1286839

Engel K.J., Fragnelli G. Analyticity of Demigroups Generated by Operators with Generalized Wentzell Boundary Conditions. Advances in Differential Equations, 2005, vol. 10, no. 11, pp. 1301–1320.

Favini A., Goldstein G.R., Romanelli S. C0 Semigroups Generated by Second Order Differential Operators with General Wentzell Boundary Conditions. Proceedings of the American Mathematical Society, 2000, vol. 128, no. 7, pp. 1981–1989. DOI: 10.1090/S0002993900054861

Favini A., Goldstein G.R., Goldstein J.A., Romanelli S. The Heat Equation with Generalized Wentzell Boundary Condition. Journal of Evolution Equations, 2002, vol. 2, pp. 1–19. DOI: 10.1007/s000280028077y

Favini A., Goldstein G.R., Goldstein J.A., Romanelli S. Classification of General Wentzell Boundary Conditions for Fourth Order Operators in One Space Dimension. Journal of Mathematical Analysis and Applications, 2007, vol. 333, no. 1, pp. 219–235. DOI: 10.1016/j.jmaa.2006.11.058

Gal C.G., Goldstein G.R., Goldstein J.A., Romanelli S. Fredholm Alternative, Semilinear Eliptic problems, and Wentzell Boundary Conditions, http://arxiv.org/abs/1311.3134.

Goldstein G.R. Derivation and Physical Interpretation of General Boundary Conditions. Advances in Difference Equations, 2006, vol. 4, no. 11, pp. 419–456. DOI: 10.57262/ade/1355867704

Favini A., Goldstein G.R., Goldstein J.A., Obrecht E., Romanelli S. The Laplacian with Generalized Wentzell Boundary Conditions. Progress in Nonlinear Differential Equations and Their Applications, 2003, vol. 55, pp. 169–180. DOI: 10.1007/9783034880855_13

Amosov A., Krymov N.On a Nonlinear Initial–Boundary Value Problem with Venttsel Type Boundary Conditions Arizing in Homogenization of Complex Heat Transfer Problems. Mathematics, 2022, vol. 10, no. 1890. DOI: 10.3390/math10111890

Diaz J.I., Tello L. On a Parabolic Problem with Diffusion on Boundary Arising in Climatology. International Conference on Differential equations, Ed, World Scientific, New Jersey, 2005, pp. 1056–1058. DOI: 10.1142/9789812702067_0179

Luo Y. Optimal Wentzell Boundary Control of Parabolic Equations. Applied

Mathematics & Optimization, 2017, vol. 75, pp. 151–173. DOI: 10.1007/s0024501593260


Refbacks

  • There are currently no refbacks.


 Save