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New results on IBVP for Class of Nonlinear Parabolic Equations

Yıl 2018, Cilt: 2 Sayı: 4, 202 - 216, 24.12.2018
https://doi.org/10.31197/atnaa.417824

Öz

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.

Kaynakça

  • [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.
Yıl 2018, Cilt: 2 Sayı: 4, 202 - 216, 24.12.2018
https://doi.org/10.31197/atnaa.417824

Öz

Kaynakça

  • [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.
Toplam 13 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Articles
Yazarlar

Svetlin G. Georgiev Bu kişi benim

Khaled Zennir

Yayımlanma Tarihi 24 Aralık 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 2 Sayı: 4

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