The Fourth Main Boundary Value Problem of Dynamics of Thermo-resiliency’s Momentum Theory

• Main Authors: Merab Aghniashvili, Diana Mtchedlishvili
• Format: Article
• Language: Russian
• Published: Academic Publishing House Researcher 2014-08-01
• Series: Evropejskij Issledovatelʹ
• Subjects: the main boundary value problem; initial conditions; boundary conditions; the uniqueness theorem of the solution
• Online Access: http://www.erjournal.ru/journals_n/1409224318.pdf

In the paper is presented the fourth main boundary value problem of Dynamics of Thermo-resiliency’s Momentum theory. The problem states to find in the cylinder D_l the regular solution of the system: M(∂_x )U-νχθ-χ^0 (∂^2 U)/(∂t^2 )=H, ∆θ-1/ϑ ∂θ/∂t-η ∂/∂t div u=H_7, which satisfies the initial conditions: 〖∀x∈D: lim〗┬(t→0)⁡〖U(x,t)=φ^((0) ) (x),〗 lim┬(t→0)⁡〖θ(x,t)=φ_7^((0) ) (x), lim┬(t→0) ∂U(x,t)/∂t=φ^((1) ) 〗 (x) and the boundary conditions: 〖∀(x,t)∈S_l:lim┬(D∋x→y∈S)〗⁡〖PU=f, 〗 lim┬(D∋x→y∈S) {θ}_S^±=f_7. The uniqueness theorem of the solution is proved for this problem.