EN
New results on IBVP for Class of Nonlinear Parabolic Equations
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
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.
Details
Primary Language
English
Subjects
Mathematical Sciences
Journal Section
Research Article
Publication Date
December 24, 2018
Submission Date
April 22, 2018
Acceptance Date
December 7, 2018
Published in Issue
Year 2018 Volume: 2 Number: 4
Cited By
On a final value problem for parabolic equation on the sphere with linear and nonlinear source
Advances in the Theory of Nonlinear Analysis and its Application
https://doi.org/10.31197/atnaa.753458