Name
Abstract | ||
|---|---|---|
We investigate the Cauchy problem for linear, constant-coefficient evolution PDEs on the real line with discontinuous initial conditions (ICs) in the small-time limit. The small-time behavior of the solution near discontinuities is expressed in terms of universal, computable special functions. We show that the leading-order behavior of the solution of dispersive PDEs near a discontinuity of the ICs is characterized by Gibbs-type oscillations and gives exactly the Wilbraham-Gibbs constants. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1137/16M1090892 | SIAM JOURNAL ON APPLIED MATHEMATICS |
Keywords | Field | DocType |
asymptotic expansions,dispersive PDEs,Gibbs phenomenon,steepest descent | Gibbs phenomenon,Oscillation,Mathematical optimization,Gradient descent,Classification of discontinuities,Mathematical analysis,Real line,Special functions,Discontinuity (linguistics),Initial value problem,Mathematics | Journal |
Volume | Issue | ISSN |
77 | 3 | 0036-1399 |
Citations | PageRank | References |
1 | 0.41 | 1 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Gino Biondini | 1 | 5 | 3.69 |
| Thomas Trogdon | 2 | 6 | 3.29 |