The existence of the global solutions to semilinear wave equations with a class of cubic nonlinearities in 2-dimensional space (Q1012983)
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scientific article; zbMATH DE number 5548680
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The existence of the global solutions to semilinear wave equations with a class of cubic nonlinearities in 2-dimensional space |
scientific article; zbMATH DE number 5548680 |
Statements
The existence of the global solutions to semilinear wave equations with a class of cubic nonlinearities in 2-dimensional space (English)
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28 April 2009
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The paper deals with the Cauchy problem of a semilinear wave equation with small initial data of compact supports in \(\mathbb R^2\). The nonlinearity, which depends only on the derivatives of the solution, is assumed to be cubic. The author shows global solvability of the problem and asymptotic behavior of the solution for the nonlinearity not being of null-form.
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null-condition
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asymptotic behavior
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small initial data
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