Problem without initial conditions for some classes of nonlinear parabolic equations

Questions of uniqueness and existence of solutions of the problem without initial conditions for quasilinear parabolic equations of arbitrary order with monotone spatial part, equations of nonstationary filtration type, and operator differential equations of parabolic type are studied. The cases when restrictions are and are not imposed on the behavior of solutions as t– are considered here.Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 14, pp. 3–44, 1989.     

Linear First-Order Evolution Problems Without Initial Conditions

Direct and inverse problems for first-order in time linear evolution problems without initial conditions, i.e. related to the unbounded time-intervals (−∞, 0] and \mathbbR{\mathbb{R}}, are considered in the framework of Banach spaces. Some degenerate in time problems related to a bounded time-interval are also considered. The approach for solving the previous problems is related to both C ₀-and Analytic Semigroup Theory.     

Correctness of the first boundary-value problem and the Cauchy problem for some quasilinear parabolic systems without conditions at infinity

In the article, questions of the uniqueness of solutions of boundary-value problems and the Cauchy problem for parabolic systems without conditions on their behavior at infinity are studied. The continuous dependence of generalized solutions of the problems considered on the right-hand terms is proved. __________ Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 25, pp. 35–54, 2005.     

Problems for parabolic equations with variable exponents of nonlinearity and time delay

The initial-boundary value problems for parabolic equations with variable exponents of nonlinearity and time depended delay are considered. Existence and uniqueness of solutions of these problems are proved.     

The unique solvability of a problem without initial conditions for linear and nonlinear elliptic-parabolic equations

The existence and the uniqueness of generalized solutions of a problem without initial conditions are established for linear and nonlinear anisotropic elliptic-parabolic second-order equations in domains unbounded in spatial variables. We put the restrictions on the behavior of solutions of the problem and the growth of its initial data at infinity. The equations have the nonlinearity exponents depending on points of the domain of definition and the direction of differentiation. Their weak solutions are taken from generalized Lebesgue–Sobolev spaces.     

Synthesis of oligosiloxane methacrylates and their application to anaerobic sealants

The synthesis of oligosiloxane methacrylates via the transesterification of oligomethoxyphenylmethylsiloxanes by 1,2-hydroxyethyl methacrylate is described. The dependences of the properties of synthesized oligomers on the content of methacrylate fragments are studied. The possibility of creating thermally stable anaerobic sealants with the required properties is shown on their basis.