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 |
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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 |
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