In the present paper, we prove the blow-up in finite time for local solutions of a semilinear Cauchy problem associated with a wave equation in anti-de Sitter spacetime in the critical case. According to this purpose, we combine a result for ordinary differential inequalities with an iteration argument by using an explicit integral representation formula for the solution to a linear Cauchy problem associated with the wave equation in anti-de Sitter spacetime in one space dimension.
On a semilinear wave equation in anti-de Sitter spacetime: The critical case
Palmieri, Alessandro
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2022-01-01
Abstract
In the present paper, we prove the blow-up in finite time for local solutions of a semilinear Cauchy problem associated with a wave equation in anti-de Sitter spacetime in the critical case. According to this purpose, we combine a result for ordinary differential inequalities with an iteration argument by using an explicit integral representation formula for the solution to a linear Cauchy problem associated with the wave equation in anti-de Sitter spacetime in one space dimension.File in questo prodotto:
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