New results on IBVP for Class of Nonlinear Parabolic Equations

Year 2018, Volume: 2 Issue: 4, 202 - 216, 24.12.2018

Svetlin G. Georgiev Khaled Zennir

https://doi.org/10.31197/atnaa.417824

Cited By: 2

Abstract

In this article we propose a new approach for investigation the local existence of classical solutions of IBVP for a class of nonlinear parabolic equations.

Keywords

nonlinear parabolic equation, local existence, classical solutions

References

• [1] K.Deng, Comparison principle for some nonlocal problems, Quart. Appl. Math. 50 (1992), no. 3, 517-522.
• [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.
• [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.
• [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.
• [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.
• [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.
• [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.
• [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.
• [9] D. Liu, Blow-up for a degenerate and singular parabolic equation with nonlocal boundary condition, J. Nonlinear Sci. Appl. 9 (2016), 208-218.
• [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.
• [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.
• [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.
• [13] Xiang, T., Rong Yuan. A class of expansive-type Krasnosel’skii fixed point theorems. Nonlinear Analysis, 71(2009), 3229- 3239.