The Cauchy Problem for the Second Order Semilinear Sobolev Type Equation
作者: Alyona A.Zamyshlyaeva Evgenij V.Bychkov
刊名: Global and Stochastic Analysis, 2015, Vol.2 (2)
来源数据库: Mind Reader Publications
关键词: phase spacesemilinear Sobolev type equationrelatively polynomially bounded operator pencilBanach manifold.
原始语种摘要: 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 and by A.A. Zamyshlyaeva for the investigation of the high-order linear Sobolev type equations. We also use the theory of differential manifolds following, say, Lang’s books. In the article we consider two cases. The first one is where an operator A at the highest time derivative is continuously invertible. In this case for any point from the tangent bundle of the original Banach space there exists a unique solution lying in this space as a trajectory. The second case, where the operator A is not continuously...
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关键词翻译
关键词翻译
  • 溶解度 半线性的
  • operator 话务员
  • admissible 容许的
  • resolvent 豫解式
  • boundedness 有界性
  • invertible 可逆
  • semilinear 半线性的
  • solvability 半线性的
  • derivative 衍生物
  • infinity 无穷限大
  • defined 定义