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 |
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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 |
Keywords
- Hamiton-Jacobi equations
- Infinite system
- Perturbed test functions
- Singular limit
- Viscosity solutions
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Applied Mathematics