The Cauchy Problem for the Heat Equation with a Random Right Part from the Space Subφ (Ω)

Show more

References

[1] de Feriet, K. (1962) Statistical Mechanics of Continuous Media. Proceedings of Symposia in Applied Mathematics, American Mathematical Society, Providence, 165-198.

[2] Beisenbaev, E. and Kozachenko, Yu.V. (1979) Uniform Convergence in Probability of Random Series, and Solutions of Boundary Value Problems with Random Initial Conditions. Theory of Probability and Mathematical Statistics, 21, 9-23.

[3] Buldygin, V.V. and Kozachenko, Yu.V. (1979) On a Question of the Applicability of the Fourier Method for Solving Problems with Random Boundary Conditions. Random Processes in Problems Mathematical Physics, Academy of Sciences of Ukrain.SSR, Institute of Mathematics, Kuiv, 4-35.

[4] de La Krus, E.B. and Kozachenko, Yu.V. (1995) Boundary-Value Problems for Equations of Mathematical Physics with Strictly Orlics Random Initial Conditios. Random Operators and Stochastic Equations, 3, 201-220.

http://dx.doi.org/10.1515/rose.1995.3.3.201

[5] Kozachenko, Yu.V. and Endzhyrgly (1994) Justification of Applicability of the Fourier Method to the Boundary-Value Problems with Random Initial Conditions I. Theory of Probability and Mathematical Statistics, 51, 78-89.

[6] Kozachenko, Yu.V. and Endzhyrgly (1994) Justification of Applicability of the Fourier Method to the Boundary-Value Problems with Random Initial Conditions II. Theory of Probability and Mathematical Statistics, 53, 58-68.

[7] Kozachenko, Yu.V. and Kovalchuk, Ya.A. (1998) Boundary Value Problems with Random Initial Conditions and Series of Functions of Subφ(Ω). Ukrainian Mathematical Journal, 50, 504-515.

[8] Dovgay, B.V., Kozachenko, Yu.V. and Slyvka-Tylyshchak, G.I. (2008) The Boundary-Value Problems of Mathematical Physics with Random Factors. Kyiv University, Kyiv, 173 p. (Ukrainian)

[9] Kozachenko, Yu.V. and Slyvka, G.I. (2004) Justification of the Fourier Method for Hyperbolic Equations with Random Initial Conditions. Theory of Probability and Mathematical Statistics, 69, 67-83.

http://dx.doi.org/10.1090/S0094-9000-05-00615-0

[10] Slyvka, A.I. (2002) A Boundary-Value Problem of the Mathematical Physics with Random Initials Conditions. Bulletin of University of Kyiv. Series: Physics & Mathematics, 5, 172-178.

[11] Slyvka-Tylyshchak, A.I. (2012) Justification of the Fourier Method for Equations of Homogeneous String Vibration with Random Initial Conditions. Annales Universitatis Scientarium Budapestinensis de Rolando Eötvös Nominatae Sectio Mathematica, 38, 211-232.

[12] Kozachenko, Y.V. and Slyvka, G.I. (2007) Modelling a Solution of a Hyperbolic Equation with Random Initial Conditions. Theory Probability and Mathematical Statistics, 74, 59-75.

[13] Tylyshchak, A.I.S. (2012) Simulation of Vibrations of a Rectangular Membrane with Random Initial Conditions. Annales Mathematicae and Informaticae, 39, 325-338.

[14] Dovgay, B.V. and Kozachenko, Y.V. (2005) The Condition for Application of Fourie Method to the Solution of Nongomogeneous String Oscillation Equation with φ-Subgaussianright Hand Side. Random Operators and Stochastic Equations, 13, 281-296.

[15] Kozachenko, Y.V. and Veresh, K.J. (2010) The Heat Equation with Random Initial Conditions from Orlicz Space. Theory of Probability and Mathematical Statistics, 80, 71-84.

http://dx.doi.org/10.1090/S0094-9000-2010-00795-2

[16] Kozachenko, Y.V. and Veresh, K.J. (2010) Boundary-Value Problems for a Nonhomogeneous Parabolic Equation with Orlicz Right Side. Random Operators and Stochastic Equations, 18, 97-119.

http://dx.doi.org/10.1515/rose.2010.005

[17] Angulo, J.M., Ruiz-Medina, M.D., Anh, V.V. and Grecksch, W. (2000) Fractional Diffusion and Fractional Heat Equation. Advances in Applied Probability, 32, 1077-1099.

http://dx.doi.org/10.1239/aap/1013540349

[18] Kozachenko, Y.V. and Leonenko, G.M. (2006) Extremal Behavior of the Heat Random Field. Extremes, 8, 191-205.

http://dx.doi.org/10.1007/s10687-006-7967-8

[19] Beghin, L., Kozachenko, Y., Orsingher, E. and Sakhno, L. (2007) On the Solution of Linear Odd-Order Heat-Type Equations with Random Initial. Journal of Statistical Physics, 127, 721-739.

http://dx.doi.org/10.1007/s10955-007-9309-x

[20] Ratanov N.E., Shuhov, A.G. and Suhov, Y.M. (1991) Stabilization of the Statistical Solution of the Parabolic Equation. Acta Applicandae Mathematicae, 22, 103-115.

[21] Buldygin, V.V. and Kozachenko, Y.V. (2000) Metric Characterization of Random Variables and Random Processes. American Mathematical Society, Rhode.

[22] Antonini, R.G., Kozachenko, Y. and Nikitina, T. (2003) Spaces of φ-Subgaussian Random Variables. Memorie di Matematica e Applicazioni, Accademia Nazionale delle Scinze detta dei XL, Vol. 27, 95-124.

[23] Krasnoselsky, M.A. and Rutitcky, Y.B. (1961) Convex Functions and Orlicz Spaces. Noordhof, Gröningen.

[24] Kozachenko, Y.V. and Ostrovskij, E.V. (1986) Banach Spaces of Random Variables of Sub-Gaussian Type. Theory of Probability and Mathematical Statistics, 532, 42-53.

[25] Markovich, B.M. (2010) Equations of Mathematical Physics. Lviv Polytechnic Publishing House, Lviv, 384 p. (Ukrainian).

[26] Budylin, A.M. (2002) Fourier Series and Integrals. Saint Petersburg, 137 p.