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New results on IBVP for Class of Nonlinear Parabolic Equations

Year 2018, , 202 - 216, 24.12.2018
https://doi.org/10.31197/atnaa.417824

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.

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.
Year 2018, , 202 - 216, 24.12.2018
https://doi.org/10.31197/atnaa.417824

Abstract

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.
There are 13 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Svetlin G. Georgiev This is me

Khaled Zennir

Publication Date December 24, 2018
Published in Issue Year 2018

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