Lower bound for the life-span of higher dimensional semilinear wave equation (Q2720943)
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scientific article; zbMATH DE number 1611743
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Lower bound for the life-span of higher dimensional semilinear wave equation |
scientific article; zbMATH DE number 1611743 |
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1 July 2001
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small initial data
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Lower bound for the life-span of higher dimensional semilinear wave equation (English)
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The authors consider the Cauchy problem with \( \varepsilon > 0 \) small initial data for the multidimensional (\( n \geq 4 \)) semilinear wave equation. The initial data belong to some suitable Sobolev spaces and the right hand side of the equation is of the type \( |u|^{p} \). Assuming the exponent \( p > 1 \) to be subcritical a lower bound for the life-span \( T(\varepsilon) \) of the weak solutions to the Cauchy problem under investigation is found.
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