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Izv. RAN. Ser. Mat., 2020, Volume 84, Issue 5, Pages 119–150 (Mi izv8880)  

Blow-up and global solubility in the classical sense of the Cauchy problem for a formally hyperbolic equation with a non-coercive source

M. O. Korpusovab

a Lomonosov Moscow State University
b Peoples' Friendship University of Russia, Moscow

Abstract: We consider an abstract Cauchy problem with non-linear operator coefficients and prove the existence of a unique non-extendable classical solution. Under certain sufficient close-to-necessary conditions, we obtain finite-time blow-up conditions and upper and lower bounds for the blow-up time. Moreover, under certain sufficient close-to-necessary conditions, we obtain a result on the existence of a global-in-time solution independently of the size of the initial functions.

Keywords: non-linear Sobolev-type equations, blow-up, local solubility, non-linear capacity, bounds for the blow-up time.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 5-100
This paper was written with the support of the PFUR Programme ‘5-100’.


DOI: https://doi.org/10.4213/im8880

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English version:
Izvestiya: Mathematics, 2020, 84:5, 930–959

Bibliographic databases:

UDC: 517.538
MSC: 35B44, 35L15, 35L71, 35L90
Received: 05.11.2018
Revised: 19.03.2019

Citation: M. O. Korpusov, “Blow-up and global solubility in the classical sense of the Cauchy problem for a formally hyperbolic equation with a non-coercive source”, Izv. RAN. Ser. Mat., 84:5 (2020), 119–150; Izv. Math., 84:5 (2020), 930–959

Citation in format AMSBIB
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\vol 84
\issue 5
\pages 119--150
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