On the behavior of solutions to a certain hyperbolic problem (Q1972645)
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scientific article; zbMATH DE number 1431676
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the behavior of solutions to a certain hyperbolic problem |
scientific article; zbMATH DE number 1431676 |
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On the behavior of solutions to a certain hyperbolic problem (English)
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13 April 2000
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The article deals with some qualitative properties of solutions to first-order weakly-nonlinear hyperbolic equations in two variables. Some sufficient conditions are stated for existence of periodic solutions. On assuming the existence of a Lyapunov functional the author proves that \(C^2\)-bounded solutions stabilize to some stationary solution. In addition, \(C^1\)- and \(C^2\)-stability is demonstrated for the stationary solution. The author also provides some examples of mathematical models of chemical reactors to which the above theorems apply.
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hyperbolic system
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periodic solution
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stabilization
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Lyapunov stability
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