TY  - JOUR
T1  - New results on IBVP for Class of Nonlinear Parabolic Equations
AU  - G. Georgiev, Svetlin
AU  - Zennir, Khaled
PY  - 2018
DA  - December
DO  - 10.31197/atnaa.417824
JF  - Advances in the Theory of Nonlinear Analysis and its Application
JO  - ATNAA
PB  - Erdal KARAPINAR
WT  - DergiPark
SN  - 2587-2648
SP  - 202
EP  - 216
VL  - 2
IS  - 4
LA  - en
AB  - In this article we propose a new approach for investigation the localexistence of classical solutions of IBVP for a class of nonlinear parabolicequations.
KW  - nonlinear parabolic equation
KW  - local existence
KW  - classical solutions
CR  - [1] K.Deng, Comparison principle for some nonlocal problems, Quart. Appl. Math. 50 (1992), no. 3, 517-522.
CR  - [2] Z.B.Fang and J. Zhang, Global and blow-up solutions for the nonlocal p-Laplacian evolution equationwith weighted nonlinear
nonlocal boundary condition, J. Integral Equat. Appl. 26 (2014), no. 2, 171-196.
CR  - [3] Y.Gao and W.Gao, Existence and blow-up of solutions for a porous medium equation with nonlocal boundary condition,
Appl. Anal. 90 (2011), no. 5, 799-809.
CR  - [4] A.Gladkov and M.Guedda, Blow-up problem for semilinear heat equation with absorption and a nonlocal boundary condition,
Nonlinear Anal. 74 (2011), no. 13, 4573-4580.
CR  - [5] A.Gladkov and M.Guedda, Semilinear heat equation with absorption and a nonlocal bound- ary condition, Appl. Anal. 91
(2012), no. 12, 2267-2276.
CR  - [6] A.Gladkov and K. I.Kim, Blow-up of solutions for semilinear heat equation with nonlinear nonlocal boundary condition,
J. Math. Anal. Appl. 338 (2008), 264-273.
CR  - [7] A.Gladkov and K. I.Kim, Uniqueness and nonuniqueness for reaction-diffusion equation with nonlocal boundary condition,
Adv. Math. Sci. Appl. 19 (2009), no. 1, 39-49.
CR  - [8] A.Gladkov and A.Nikitin, A reaction-diffusion system with nonlinear nonlocal boundary conditions, Int. J. Partial Differential
Equations 2014 (2014), Article ID 523656, 10 pages.
CR  - [9] D. Liu, Blow-up for a degenerate and singular parabolic equation with nonlocal boundary condition, J. Nonlinear Sci.
Appl. 9 (2016), 208-218.
CR  - [10] D. Liu and C.Mu, Blowup properties for a semilinear reaction-diffusion system with nonlinear nonlocal boundary conditions,
Abstr. Appl. Anal. 2010 (2010), Article ID 148035, 17 pages.
CR  - [11] G. Zhong and L.Tian Blow up problems for a degenerate parabolic equation with nonlocal source and nonlocal nonlinear
boundary condition, Boundary Value Problems 2012 (2012), no. 45, 14 pages.
CR  - [12] J. Zhou and D.Yang Blowup for a degenerate and singular parabolic equation with nonlocal source and nonlocal boundary,
Appl. Math. Comput. 256 (2015), 881-884.
CR  - [13] Xiang, T., Rong Yuan. A class of expansive-type Krasnosel’skii fixed point theorems. Nonlinear Analysis, 71(2009), 3229-
3239.
UR  - https://doi.org/10.31197/atnaa.417824
L1  - https://dergipark.org.tr/en/download/article-file/594215
ER  -