Abstract
We study the asymptotic behavior of solutions of the Cauchy problem for a functional partial differential equation with a small parameter as the parameter tends to zero. We establish a convergence theorem in which the limit problem is identified with the Cauchy problem for a nonlinear parabolic partial differential equation. We also present comparison and existence results for the Cauchy problem for the functional partial differential equation and the limit problem.
| Original language | English |
|---|---|
| Pages (from-to) | 409-438 |
| Number of pages | 30 |
| Journal | Communications in Partial Differential Equations |
| Volume | 28 |
| Issue number | 1-2 |
| Publication status | Published - 2003 |
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Keywords
- Hamiton-Jacobi equations
- Infinite system
- Perturbed test functions
- Singular limit
- Viscosity solutions
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Applied Mathematics
Cite this
Ishii, H., & Shimano, K. (2003). Asymptotic analysis for a class of infinite systems of first-order PDE: Nonlinear parabolic PDE in the singular limit. Communications in Partial Differential Equations, 28(1-2), 409-438.