Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2021, , 118 - 127, 31.07.2021
https://doi.org/10.33773/jum.962057

Öz

Kaynakça

  • R.A. Adams and J.J.F. Fournier, Sobolev Spaces, Academic Press, (2003).
  • H. Chen, P. Luo, G. Liu, Global solution and blow-up of a semilinear heat equation with logarithmic nonlinearity, Journal of Mathematical Analysis and Applications, 422(1), 84-98, (2015).
  • H. Chen, S. Tian, Initial boundary value problem for a class of semilinear pseudo-parabolic equations with logarithmic nonlinearity, Journal of Differential Equations, 258, 4424-4442, (2015).
  • V.A. Galaktionov, Critical global asymptotics in higher-order semilinear parabolic equations, International Journal of Mathematics and Mathematical Sciences, 60, 3809-3825, (2003).
  • Y. Han, Blow-up at infinity of solutions to a semilinear heat equation with logarithmic nonlinearity, Journal of Mathematical Analysis and Applications, 471, 513-517, (2019).
  • Y. He, H. Gao, H. Wang, Blow-up and decay for a class of pseudo-parabolic p-Laplacian equation with logarithmic nonlinearity, Computers & Mathematics with Applications, 75, 459-469, (2018).
  • K. Ishige, T. Kawakami, S. Okabe, Existence of solutions for a higher-order semilinear parabolic equation with singular initial data, Annales de l'Institut Henri Poincare C, Analyse Nonlineaire, 37, 1185-1209, (2020).
  • P. Li, C. Liu, A class of fourth-order parabolic equation with logarithmic nonlinearity, Journal of Inequalities and Applications, 328, 1-21, (2018).
  • L.C. Nhan, L.X. Truong, Global solution and blow-up for a class of pseudo p-Laplacian evolution equations with logarithmic nonlinearity, Computers & Mathematics with Applications, 73, 2076-2091, (2017).
  • J. Peng, J. Zhou, Global existence and blow-up of solutions to a semilinear heat equation with logarithmic nonlinearity, Applicable Analysis, 1-21, (2019).
  • E. Pişkin, N. Polat, On the decay of solutions for a nonlinear higher-order Kirchhoff-type hyperbolic equation, Journal of Advanced Research in Applied Mathematics, 5(2), 107-116, (2013).
  • E. Pişkin, Blow up solutions for a class of nonlinear higher-order wave equation with variable exponents, Sigma Journal of Engineering and Natural Sciences, 10(2), 149-156, (2019).
  • L. Xiao, M. Li, Initial boundary value problem for a class of higher-order n-dimensional nonlinear pseudo-parabolic equations, Boundary Value Problems, 5, 1-24, (2021).
  • Y. Ye, Existence and asymptotic behaviour of global solutions for a class of nonlinear higher-order wave equation, Journal of Inequalities and Applications, 1-14, (2010).
  • J. Zhou, X. Wang, X. Song, C. Mu, Global existence and blowup of solutions for a class of nonlinear higher-order wave equations, Zeitschrift für Angewandte Mathematik und Physik, 63, 461-473, (2012).

BLOW UP AT INFINITY OF WEAK SOLUTIONS FOR A HIGHER-ORDER PARABOLIC EQUATION WITH LOGARITHMIC NONLINEARITY

Yıl 2021, , 118 - 127, 31.07.2021
https://doi.org/10.33773/jum.962057

Öz

The main goal of this work is to study the inital boundary value problem for a higher-order parabolic equation with logarithmic source term
u_{t}+(-\Delta )^{m}u=uln (u).
We obtain blow-up at infinity of weak solutions, by employing potential well technique. This improves and extends some previous studies.

Kaynakça

  • R.A. Adams and J.J.F. Fournier, Sobolev Spaces, Academic Press, (2003).
  • H. Chen, P. Luo, G. Liu, Global solution and blow-up of a semilinear heat equation with logarithmic nonlinearity, Journal of Mathematical Analysis and Applications, 422(1), 84-98, (2015).
  • H. Chen, S. Tian, Initial boundary value problem for a class of semilinear pseudo-parabolic equations with logarithmic nonlinearity, Journal of Differential Equations, 258, 4424-4442, (2015).
  • V.A. Galaktionov, Critical global asymptotics in higher-order semilinear parabolic equations, International Journal of Mathematics and Mathematical Sciences, 60, 3809-3825, (2003).
  • Y. Han, Blow-up at infinity of solutions to a semilinear heat equation with logarithmic nonlinearity, Journal of Mathematical Analysis and Applications, 471, 513-517, (2019).
  • Y. He, H. Gao, H. Wang, Blow-up and decay for a class of pseudo-parabolic p-Laplacian equation with logarithmic nonlinearity, Computers & Mathematics with Applications, 75, 459-469, (2018).
  • K. Ishige, T. Kawakami, S. Okabe, Existence of solutions for a higher-order semilinear parabolic equation with singular initial data, Annales de l'Institut Henri Poincare C, Analyse Nonlineaire, 37, 1185-1209, (2020).
  • P. Li, C. Liu, A class of fourth-order parabolic equation with logarithmic nonlinearity, Journal of Inequalities and Applications, 328, 1-21, (2018).
  • L.C. Nhan, L.X. Truong, Global solution and blow-up for a class of pseudo p-Laplacian evolution equations with logarithmic nonlinearity, Computers & Mathematics with Applications, 73, 2076-2091, (2017).
  • J. Peng, J. Zhou, Global existence and blow-up of solutions to a semilinear heat equation with logarithmic nonlinearity, Applicable Analysis, 1-21, (2019).
  • E. Pişkin, N. Polat, On the decay of solutions for a nonlinear higher-order Kirchhoff-type hyperbolic equation, Journal of Advanced Research in Applied Mathematics, 5(2), 107-116, (2013).
  • E. Pişkin, Blow up solutions for a class of nonlinear higher-order wave equation with variable exponents, Sigma Journal of Engineering and Natural Sciences, 10(2), 149-156, (2019).
  • L. Xiao, M. Li, Initial boundary value problem for a class of higher-order n-dimensional nonlinear pseudo-parabolic equations, Boundary Value Problems, 5, 1-24, (2021).
  • Y. Ye, Existence and asymptotic behaviour of global solutions for a class of nonlinear higher-order wave equation, Journal of Inequalities and Applications, 1-14, (2010).
  • J. Zhou, X. Wang, X. Song, C. Mu, Global existence and blowup of solutions for a class of nonlinear higher-order wave equations, Zeitschrift für Angewandte Mathematik und Physik, 63, 461-473, (2012).
Toplam 15 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Araştırma Makalesi
Yazarlar

Tuğrul Cömert 0000-0002-8176-332X

Erhan Pişkin 0000-0001-6587-4479

Yayımlanma Tarihi 31 Temmuz 2021
Gönderilme Tarihi 3 Temmuz 2021
Kabul Tarihi 27 Temmuz 2021
Yayımlandığı Sayı Yıl 2021

Kaynak Göster

APA Cömert, T., & Pişkin, E. (2021). BLOW UP AT INFINITY OF WEAK SOLUTIONS FOR A HIGHER-ORDER PARABOLIC EQUATION WITH LOGARITHMIC NONLINEARITY. Journal of Universal Mathematics, 4(2), 118-127. https://doi.org/10.33773/jum.962057
AMA Cömert T, Pişkin E. BLOW UP AT INFINITY OF WEAK SOLUTIONS FOR A HIGHER-ORDER PARABOLIC EQUATION WITH LOGARITHMIC NONLINEARITY. JUM. Temmuz 2021;4(2):118-127. doi:10.33773/jum.962057
Chicago Cömert, Tuğrul, ve Erhan Pişkin. “BLOW UP AT INFINITY OF WEAK SOLUTIONS FOR A HIGHER-ORDER PARABOLIC EQUATION WITH LOGARITHMIC NONLINEARITY”. Journal of Universal Mathematics 4, sy. 2 (Temmuz 2021): 118-27. https://doi.org/10.33773/jum.962057.
EndNote Cömert T, Pişkin E (01 Temmuz 2021) BLOW UP AT INFINITY OF WEAK SOLUTIONS FOR A HIGHER-ORDER PARABOLIC EQUATION WITH LOGARITHMIC NONLINEARITY. Journal of Universal Mathematics 4 2 118–127.
IEEE T. Cömert ve E. Pişkin, “BLOW UP AT INFINITY OF WEAK SOLUTIONS FOR A HIGHER-ORDER PARABOLIC EQUATION WITH LOGARITHMIC NONLINEARITY”, JUM, c. 4, sy. 2, ss. 118–127, 2021, doi: 10.33773/jum.962057.
ISNAD Cömert, Tuğrul - Pişkin, Erhan. “BLOW UP AT INFINITY OF WEAK SOLUTIONS FOR A HIGHER-ORDER PARABOLIC EQUATION WITH LOGARITHMIC NONLINEARITY”. Journal of Universal Mathematics 4/2 (Temmuz 2021), 118-127. https://doi.org/10.33773/jum.962057.
JAMA Cömert T, Pişkin E. BLOW UP AT INFINITY OF WEAK SOLUTIONS FOR A HIGHER-ORDER PARABOLIC EQUATION WITH LOGARITHMIC NONLINEARITY. JUM. 2021;4:118–127.
MLA Cömert, Tuğrul ve Erhan Pişkin. “BLOW UP AT INFINITY OF WEAK SOLUTIONS FOR A HIGHER-ORDER PARABOLIC EQUATION WITH LOGARITHMIC NONLINEARITY”. Journal of Universal Mathematics, c. 4, sy. 2, 2021, ss. 118-27, doi:10.33773/jum.962057.
Vancouver Cömert T, Pişkin E. BLOW UP AT INFINITY OF WEAK SOLUTIONS FOR A HIGHER-ORDER PARABOLIC EQUATION WITH LOGARITHMIC NONLINEARITY. JUM. 2021;4(2):118-27.