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作者:Alyona A.Zamyshlyaeva , Evgenij V.Bychkov
来源:[J].Global and Stochastic Analysis, 2015, Vol.2 (2)Mind Reader Publications
摘要:We prove a unique solvability of the Cauchy problem for a class of second order semilinear Sobolev type equations. We use ideas and techniques developed by G.A. Sviridyuk for the investigation of the Cauchy problem for a class of first order semilinear Sobolev type equations...
作者:G.A. Sviridyuk
来源:[J].Nonlinear Bound. Value Probl. 14, 126-137 (2004)., 2004, pp.126-137ZBMATH
摘要:Summary: The solvability of the Cauchy problem $u(0)=u_0$ of an semilinear differential operator equation $L\dot u = Mu + N(u)$ is under consideration. The abstract results are illustrated by the Cauchy -- Dirichlet problem for the Hoff equation and for the Oskolkov equations.
作者:Elena I. Kaikina
来源:[J].Nonlinear Anal., Theory Methods Appl., 2007, Vol.67 (10), pp.2839-2858ZBMATH
摘要:The main results of this paper are the proof of the global existence of solutions to an initial-boundary value problem for a nonlinear pseudoparabolic type equation (which is also known as semilinear Sobolev type equation) and finding the main term of the asymptotic expansion of ...
作者:Georgy A. Sviridyuk
来源:[J].Ukr. Mat. Visn., 2004, Vol.1 (2), pp.259-272ZBMATH
摘要:Summary: The solvability of the Cauchy problem $u(0)=u_0$ for a semilinear differential operator equation $L\dot u = Mu + N(u)$ is considered. Abstract results are illustrated by the Cauchy-Dirichlet problem for degenerate reaction-diffusion equations and for Navier-Stokes equations...
作者:T.A. Bokareva
来源:[J].Differ. Equations(IF 0.42), 1996, Vol.32 (6), pp.819-825ZBMATH
摘要:The paper deals with the Cauchy problem of the semilinear Sobolev-type equation $L\dot u= Mu+F(u)$, where $L$, $M$, and $F$ are, respectively, continuous linear, closed linear, and nonlinear smooth operators acting in related Banach spaces. A specific case of this equation models...
作者:G.A. Sviridyuk
来源:[J].Ekaterinburg: Institut Matematiki i Mekhaniki UrO Rossijskoj Akademii Nauk, 35 p. (1993)., 1993ZBMATH
摘要:The investigation is concerned with the uniqueness solvability of the Cauchy problem (1) $u(0)=u\sb 0$ for a semilinear equation of Sobolev type (2) $L\dot u=Mu$, where the operator $L: U\sb L\to F$ is linear, the operator $M: U\sb M\to F$ is, in general, nonlinear and smooth, an...
作者:Yang Cao , Jingxue Yin , Chunpeng Wang
来源:[J].J. Differ. Equations(IF 1.48), 2009, Vol.246 (12), pp.4568-4590ZBMATH
摘要:The Cauchy problems $u(x,0)=u_0 (x)$, $x\in \Bbb R^n$, for semilinear Sobolev type equation $(u-\kappa \Delta u)_t = \Delta u +u^p$ in $\Bbb R^n\times\Bbb R_+$ is under consideration. Here parameters $k$, $p\in\Bbb R_+$ and function $u_0 (x)$ is nonnegative and appropriately smoo...
作者:S.A. Zagrebina , M.M. Yakupov
来源:[J].Vestn. Yuzhno-Ural. Gos. Univ. 27(127), Ser. Mat. Model. Program. 2, 10-18 (2008)., 2008, pp.10-18ZBMATH
摘要:The authors analyse the unique solvability of the Cauchy problem for a semilinear Sobolev type equation with a relatively $p$-sectorial operator, and the stability its solutions near the origin. The thermoconvection problem for the Oskolkov equation modeling the dynamics of an in...

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