Abstract
We study the existence and the large time behavior of global-intime solutions of a nonlinear integral equation with a generalized heat kernel u(x, t) = ∫RN G(x - y, t)φ(y)dy +∫t0 ZRN G(x - y, t - s)F(y, s, u(y, s), . . . ,δlu(y, s))dyds, where φ 2 ∈Wl,∞(RN) and l ∈ {0, 1, . . . }. The arguments of this paper are applicable to the Cauchy problem for various nonlinear parabolic equations such as fractional semilinear parabolic equations, higher order semilinear parabolic equations and viscous Hamilton-Jacobi equations.
| Original language | English |
|---|---|
| Pages (from-to) | 767-783 |
| Number of pages | 17 |
| Journal | Discrete and Continuous Dynamical Systems - Series S |
| Volume | 7 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 2014 Aug 1 |
Keywords
- Generalized heat kernel
- Global solutions
- Nonlinear integral equation
- Semilinear parabolic equations
- Weak Lr space
ASJC Scopus subject areas
- Analysis
- Discrete Mathematics and Combinatorics
- Applied Mathematics
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Cite this
Ishige, K., Kawakami, T., & Kobayashi, K. (2014). Global solutions for a nonlinear integral equation with a generalized heat kernel. Discrete and Continuous Dynamical Systems - Series S, 7(4), 767-783. https://doi.org/10.3934/dcdss.2014.7.767