Nonexistence of Solutions for a Logarithmic m-Laplacian Type Equation with Delay Term

In this work, we consider a logarithmic m-Laplacian type equation with delay term with initial and boundary conditions. Under suitable conditions on the initial data, we study the nonexistence of solutions in a finite time with negative initial energy $E\left( 0\right) <0$ in a bounded domain.

Keywords:

Decay term, logarithmic source term m-Laplacian equation, nonexistence of solutions,

PDF

___

K. Bartkowski, P. Gorka, One dimensional Klein-Gordon equation with logarithmic nonlinearities, J. Phys. A 41 (2008).
I. Bialynicki-Birula, J. Mycielski, Wave equations with logarithmic nonlinearities, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys., 23(4) (1975) 461-466.
I. Bialynicki-Birula, J. Mycielski, Nonlinear wave mechanics, Ann. Physics, 100(1-2) (1976) 62-93.
T. Cazenave, A. Haraux, Equations d'evolution avec non-linearite logarithmique, Ann. Fac. Sci. Toulouse Math., 2(1) (1980) 21-51.
R. Datko, J. Lagnese, M. P. Polis, An example on the effect of time delays in boundary feedback stabilization of wave equations, SIAM J. Control Optim., 24(1) (1986) 152-156.
P. Gorka, Logarithmic Klein-Gordon equation, Acta Phys. Polon. B 40 (2009) 59--66.
M. Kafini, S. A. Messaoudi, A blow-up result in a nonlinear wave equation with delay, Mediterr. J. Math., 13 (2016) 237-247. M. Kafini, S. Messaoudi, Local existence and blow up of solutions to a logarithmic nonlinear wave equation with delay, Appl. Anal., (2018) 1-18.
C.N. Le, X. T. Le, Global solution and blow up for a class of Pseudo p-Laplacian evolution equations with logarithmic nonlinearity, Comput. Math. Appl., 73(9) (2017) 2076.
N. Mezouar, S.M. Boulaaras, A. Allahem, Global existence of solutions for the viscoelastic Kirchhoff equation with logarithmic source terms, J. Complex, (2020), 1-25. S. Nicaise, C. Pignotti, Stabilization of the wave equation with boundary or internal distributed delay, Differ. Integral Equ., 21 (2008) 935-958.
S. Nicaise, C. Pignotti, Stability and instability results of the wave equation with a delay term in the boundary or internal feedbacks, SIAM J. Control Optim., 45(5) (2006) 1561-1585.
S.H. Park, Global existence, energy decay and blow-up of solutions for wave equations with time delay and logariithmic source, Adv. Differ. Equ., 2020:631 (2020) 1-17.
E. Pişkin, N. Irkıl, Mathematical behavior of solutions of p-Laplacian equation with logarithmic source term, Sigma J. Eng. & Nat. Sci., 10(2) (2019) 213-220.
E. Pişkin, H. Yüksekkaya, Nonexistence of solutions of a delayed wave equation with variable-exponents, C-POST, 3(1), 97--101, 2020. E. Pişkin, H. Yüksekkaya, Decay and blow up of solutions for a delayed wave equation with variable-exponents, C-POST, 3(1), 91--96, 2020.
E. Pişkin, H. Yüksekkaya, Local existence and blow up of solutions for a logarithmic nonlinear viscoelastic wave equation with delay, Comput. Methods Differ. Equ., 1-14, 2020, doi:10.22034/cmde.2020.35546.1608. (In press)
E. Pişkin, H. Yüksekkaya, Nonexistence of global solutions of a delayed wave equation with variable-exponents, Miskolc Math. Notes, 1-19. (Accepted)
E. Pişkin, H. Yüksekkaya, Blow-up of solutions for a logarithmic quasilinear hyperbolic equation with delay term, J. Math. Anal., 12(1), 56-64, 2021.

Yayın Aralığı: Yılda 2 Sayı
Başlangıç: 2013
Yayıncı: Mehmet Zeki SARIKAYA

Arşiv