On optimal exponential decay properties of solutions to the Korteweg–de Vries Equation
| Autor: | Carlos A. León, Pedro Isaza |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Vries equation
Applied Mathematics 010102 general mathematics Mathematical analysis Mathematics::Analysis of PDEs Function (mathematics) 01 natural sciences Dispersionless equation Nonlinear Sciences::Exactly Solvable and Integrable Systems Exponential growth 0103 physical sciences Order (group theory) Initial value problem 010307 mathematical physics 0101 mathematics Exponential decay Korteweg–de Vries equation Analysis Mathematics |
| Zdroj: | Journal of Differential Equations. 263:5189-5215 |
| ISSN: | 0022-0396 |
| DOI: | 10.1016/j.jde.2017.06.013 |
| Popis: | We consider the Cauchy problem associated to the Korteweg–de Vries equation (KdV) and study the preservation of exponential decay of order 3/2 on the right of the x-axis as time evolves. More precisely, for a solution of the equation which decays at t = 0 as e − a 0 x 3 / 2 for x > 0 , we find an optimal function a ( t ) with a ( 0 ) = a 0 such that the solution decays as e − a ( t ) x 3 / 2 for x , t > 0 . |
| Databáze: | OpenAIRE |
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