Blow-up of Solutions and Local Solvability of an Abstract Cauchy Problem of Second Order with a Noncoercive Source

An abstract Cauchy problem for a second-order differential equation with nonlinear operator coefficients is considered. The local solvability of the problem in suitable spaces of abstract continuous and differentiable functions is proved. Sufficient conditions for finite-time blow-up of its solution...

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Bibliographic Details
Published in:Computational mathematics and mathematical physics Vol. 63; no. 4; pp. 542 - 552
Main Authors: Artem’eva, M. V., Korpusov, M. O.
Format: Journal Article
Language:English
Published: Moscow Pleiades Publishing 01.04.2023
Springer Nature B.V
Subjects:
Banach spaces
Cauchy problems
Computational Mathematics and Numerical Analysis
Differential equations
Inequality
Mathematics
Mathematics and Statistics
Operators (mathematics)
Partial Differential Equations
local solvability
estimates of blow-up time
nonlinear capacity
blow-up
nonlinear Sobolev-type equations
ISSN:0965-5425, 1555-6662
Online Access:Get full text
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Summary:An abstract Cauchy problem for a second-order differential equation with nonlinear operator coefficients is considered. The local solvability of the problem in suitable spaces of abstract continuous and differentiable functions is proved. Sufficient conditions for finite-time blow-up of its solutions are obtained.
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ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542523040024