Existence of solutions of some nonlinear wave equations
type: Item
instance of: scholarly article
title: Existence of solutions of some nonlinear wave equations
zbMATH Open document ID: 0573.35061
author: Kenji Maruo
published in: Osaka Journal of Mathematics
publication date: 1985-01-01T00:00:00Z
review text: The author considers the initial value problem stated as follows: \[ d^ 2u/dt^ 2+Au+\partial \phi u\ni f(t,u),\quad t\in | 0,T|,\quad u\in H,\quad u(0)=a,\quad (d/dt)u(0)=b. \] Here t is a fixed positive number and H is a real Hilbert space while A is a positive selfadjoint operator in H, \(\phi\) is a known function from H to [-\(\infty,\infty]\), f is a given function from [0,T]\(\times H\) to H and \(\partial \phi\) is the subdifferential of \(\phi\). The main objective of the paper is to give some sufficient conditions which guarantee the existence of at least one solution. Though the paper involves some illustrative examples, it is hardly readable. Especially the meanings of some relations appearing in the definition of a solution are not clear.
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35D05
Mathematics Subject Classification ID: 47A50
Mathematics Subject Classification ID: 35L15
zbMATH DE Number: 3914844
zbMATH Keywords: initial value problem
zbMATH Keywords: existence
reviewed by: Mithat Idemen
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3914844