Blow-up instability in non-linear wave models with distributed parametersстатья
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Дата последнего поиска статьи во внешних источниках: 29 июля 2020 г.
Аннотация:We consider two model non-linear equations describing electricoscillations in systems with distributed parameters on the basis of diodeswith non-linear characteristics. We obtain equivalent integral equationsfor classical solutions of the Cauchy problem and the first and second initial-boundary value problems for the original equations in the half-spacex > 0. Using the contraction mapping principle, we prove the local-in-timesolubility of these problems. For one of these equations, we use the Pokhozhaevmethod of non-linear capacity to deduce a priori bounds giving riseto finite-time blow-up results and obtain upper bounds for the blow-uptime. For the other, we use a modification of Levine’s method to obtainsufficient conditions for blow-up in the case of sufficiently large initial dataand give a lower bound for the order of growth of a functional with themeaning of energy. We also obtain an upper bound for the blow-up time.