| Sewing Connection of Step-Step Solution for Singularly Perturbed Problems |
| Received:January 18, 2010 Revised:April 27, 2010 |
| Key Words:
sewing connection internal layer phenomenon asymptotic expansion.
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant Nos.11071075; 11171113), the Russian Foundation for Basic Research (Grant No.12-01-00256), the NSFC-the Knowledge Innovation Program of Chinese Academy of Science (Grant Nos.30921064; 90820307), Shanghai Municipal Natural Science Foundation (Grant No.10ZR1409200) and E-Institutes of Shanghai Municipal Education Commission (Grant No.E03004) |
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| Abstract: |
| In view of singularly perturbed problems with complex inner layer phenomenon, including contrast structures (step-step solution and spike-type solution), corner layer behavior and right-hand side discontinuity, we carry out the process with sewing connection. The presented method of sewing connection for singularly perturbed equations is based on the two points singularly perturbed simple boundary problems. By means of sewing orbit smoothness, we get the uniformly valid solution in the whole interval. It is easy to prove the existence of solutions and deal with the high dimensional singularly perturbed problems. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2012.01.004 |
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