No. 27 (127), issue 2Pages 10 - 18 # EXISTENCE AND STABILITY OF SOLUTIONS OF ONE CLASS OF SEMILINEAR SOBOLEV-TYPE EQUATIONS

S.A. Zagrebina, M.M. YakupovThe authors analyses the unique solvability of the Cauchy problem for the semilinear Sobolev type equation with a relatively p-sectorial operator, and the stability of solutions of this equation about a point of the origin of coordinates in case of the irreversibility of the operator under derivative, particularly when its core is nontrivial as an example of the results, the thermoconvection problem for the Oskolkov equation modeled dynamic of incompressible visco-elastic fluid is considered.

Full text- Keywords
- Oskolkov equation, Sobolev type equation, relatively p-sectorial operator, existence and stability of solutions