Description

• Title:
  Mild solutions to a class of nonlinear second order evolution equations
• Creator:
  Garcia-Falset, Jésus
• Description:
  The purpose of this paper is to study the existence of mild solutions to a class of second order nonlinear evolution equations of the form \begin{equation*} \begin{cases} u''(t)+A(u'(t))+B(u(t))\ni f(t), &t\in(0,T),\\ u(0)=u_0, \quad u'(0)=g(u') \end{cases} \end{equation*} where $A\colon D(A)\subseteq X\rightarrow 2^{X}$ is an $m$-accretive operator on a Banach space $X,$ $B: X\rightarrow X$ is a lipschitz mapping, $g\colon C([0,T];X)\to X$ is a function and $f\in L^1(0,T,X)$. We obtain sufficient conditions for this problem to have at least a mild solution.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2024 Jésus Garcia-Falset;
  https://creativecommons.org/licenses/by-nd/4.0
• Date:
  2024.03.03
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 63, No 1 (March 2024); 131 - 151;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/49145/37872 ;https://apcz.umk.pl/TMNA/article/view/49145/37873
• Subject:
  Evolution equation;
  mild solution;
  Primary: 34A34;
  Secondary 34G20
• Identifier: https://apcz.umk.pl/TMNA/article/view/49145
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other