Abstract
The Cauchy problem for nonlinear first order partial differential-functional equations in unbounded domains is treated with a general class of the method of lines. Existence and convergence properties of the method are investigated under the assumption that the right- hand side of the equation satisfies the Lipschitz condition with respect to the functional argument. The theorems are proved by means of the differential-difference inequalities technique. Examples of differential-functional problems and corresponding methods of lines are given.
| Original language | English |
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| Pages (from-to) | 413-428 |
| Number of pages | 16 |
| Journal | Studia Scientiarum Mathematicarum Hungarica |
| Volume | 34 |
| Issue number | 4 |
| State | Published - 1998 |
Keywords
- Cauchy problem
- Comparison technique
- Differential-difference inequalities
- Unbounded solutions