Description

• Title:
  Cauchy problems and applications
• Creator:
  Lin, Chin-Yuan
• Description:
  Of concern is the Cauchy problem $$ \frac{du}{dt} \in Au,\quad u(0) = u_{0},\quad t > 0, $$ where $ u : [0, \infty) \to X$, $X $ is a real Banach space, and $ A : D(A) \subset X \to X $ is nonlinear and multi-valued. It is showed by the method of lines, combined with the Crandall-Liggett theorem that this problem has a limit solution, and that the limit solution is a unique strong one if $ A $ is what is called embeddedly quasi-demi-closed. In the case of linear, single-valued $ A $, further results are given. An application to nonlinear partial differential equations in non-reflexive $ X $ is given.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2000.06.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 15, No 2 (June 2000); 359 - 368;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2000.024/9991
• Subject:
  Cauchy problems;
  operator semigroups;
  47D03;
  47H20;
  47H06
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2000.024
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other