- Research Article
- Open Access
On Comparison Principles for Parabolic Equations with Nonlocal Boundary Conditions
Boundary Value Problems volume 2007, Article number: 080929 (2007)
A generalization of the comparison principle for a semilinear and a quasilinear parabolic equations with nonlocal boundary conditions including changing sign kernels is obtained. This generalization uses a positivity result obtained here for a parabolic problem with nonlocal boundary conditions.
Yin H-M: On a class of parabolic equations with nonlocal boundary conditions. Journal of Mathematical Analysis and Applications 2004,294(2):712-728. 10.1016/j.jmaa.2004.03.021
Pao CV: Dynamics of reaction-diffusion equations with nonlocal boundary conditions. Quarterly of Applied Mathematics 1995,53(1):173-186.
Wang Y: Weak solutions for nonlocal boundary value problems with low regularity data. Nonlinear Analysis: Theory, Methods & Applications 2007,67(1):103-125. 10.1016/j.na.2006.05.002
Friedman A: Monotonic decay of solutions of parabolic equations with nonlocal boundary conditions. Quarterly of Applied Mathematics 1986,44(3):401-407.
Wang Y, Zhou C: Contraction operators and nonlocal problems. Communications in Applied Analysis 2001,5(1):31-37.
Yin YF: On nonlinear parabolic equations with nonlocal boundary condition. Journal of Mathematical Analysis and Applications 1994,185(1):161-174. 10.1006/jmaa.1994.1239
Wang Y, Nai B: Existence of solutions to nonlocal boundary problems for parabolic equations. Chinese Annals of Mathematics. Series A 1999,20(3):323-332.
Wang Y: Solutions to nonlinear elliptic equations with a nonlocal boundary condition. Electronic Journal of Differential Equations 2002,2002(5):1-16.
Wang R-N, Xiao T-J, Liang J: A comparison principle for nonlocal coupled systems of fully nonlinear parabolic equations. Applied Mathematics Letters 2006,19(11):1272-1277. 10.1016/j.aml.2006.01.012
Carl S, Lakshmikantham V: Generalized quasilinearization method for reaction diffusion equations under nonlinear and nonlocal flux conditions. Journal of Mathematical Analysis and Applications 2002,271(1):182-205. 10.1016/S0022-247X(02)00114-2