A new transform method for evolution partial differential equations |
| |
Authors: | Fokas A. S. |
| |
Affiliation: | 1 Department of Applied Mathematics and Theoretical Physics, Cambridge University, Cambridge CB3 0WA |
| |
Abstract: | We introduce a new transform method for solving initial-boundary-valueproblems for linear evolution partial differential equationswith spatial derivatives of arbitrary order. This method isillustrated by solving several such problems on the half-line{t > 0, 0 < x < }, and on the quarter-plane {t >0, 0 < xj < , j = 1, 2}. For equations in one space dimensionthis method constructs q(x, t) as an integral in the complexk-plane involving an x-transform of the initial condition anda t-transform of the boundary conditions. For equations in twospace dimensions it constructs q(x1, x2, t) as an integral inthe complex (k1, k2)-planes involving an (x1, x2)-transformof the initial condition, an (x2, t)-transform of the boundaryconditions at x1 = 0, and an (x1, t)-transform of the boundaryconditions at x2 = 0. This method is simple to implement andyet it yields integral representations which are particularlyconvenient for computing the long time asymptotics of the solution. |
| |
Keywords: | initial-boundary-value problems. |
本文献已被 Oxford 等数据库收录! |
|