Global properties of damped semilinear wave equation (Q2704781)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Global properties of damped semilinear wave equation |
scientific article |
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12 March 2001
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Klein-Gordon equation
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repellent forcing term of logarithmic form
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blow up effects
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small data
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Global properties of damped semilinear wave equation (English)
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This paper deals with the Cauchy problem for damped semilinear equations with repellent forcing term of logarithmic form \( u\ln^{q} (1+u^{2}) \), \( q > 0 \). A global existence result is proved in the case \( q \leq 2 \) and exponential decay of the small data solution for \( t \rightarrow \infty \) is shown if \( q < 2 \). Moreover, a contradecay theorem and blow up effects are established in the massless case for \( q < 2 \), respectively \( q > 2 \).
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