JOURNAL BROWSE
Search
Advanced SearchSearch Tips
GLOBAL EXISTENCE OF WEAK SOLUTIONS FOR A LOGARITHMIC WAVE EQUATION ARISING FROM Q-BALL DYNAMICS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
GLOBAL EXISTENCE OF WEAK SOLUTIONS FOR A LOGARITHMIC WAVE EQUATION ARISING FROM Q-BALL DYNAMICS
Han, Xiaosen;
  PDF(new window)
 Abstract
In this paper we investigate an initial boundary value problem of a logarithmic wave equation. We establish the global existence of weak solutions to the problem by using Galerkin method, logarithmic Sobolev inequality and compactness theorem.
 Keywords
logarithmic nonlinearity;global existence;logarithmic Sobolev inequality;logarithmic Gronwall inequality;
 Language
English
 Cited by
1.
Existence of the global solution for fractional logarithmic Schrödinger equation, Computers & Mathematics with Applications, 2017  crossref(new windwow)
2.
Asymptotic Behavior for a Class of Logarithmic Wave Equations with Linear Damping, Applied Mathematics & Optimization, 2017  crossref(new windwow)
3.
Abstract Cauchy problem for weakly continuous operators, Journal of Mathematical Analysis and Applications, 2016, 435, 1, 267  crossref(new windwow)
4.
The existence and the asymptotic behavior of a plate equation with frictional damping and a logarithmic source term, Journal of Mathematical Analysis and Applications, 2017, 454, 2, 1114  crossref(new windwow)
5.
Generation of soliton-like wave packets and wave packets with linear phase modulation in gaining optical wave-guides with saturable nonlinearity, Optics and Spectroscopy, 2017, 122, 5, 774  crossref(new windwow)
6.
Existence and a general decay result for a plate equation with nonlinear damping and a logarithmic source term, Journal of Evolution Equations, 2017  crossref(new windwow)
 References
1.
J. D. Barrow and P. Parsons, Inflationary models with logarithmic potentials, Phys. Rev. D 52 (1995), 5576-5587. crossref(new window)

2.
K. Bartkowski and P. Gorka, One-dimensional Klein-Gordon equation with logarithmic nonlinearities, J. Phys. A 41 (2008), no. 35, 355201, 11 pp. crossref(new window)

3.
I. Bialynicki-Birula and J. Mycielski, Wave equations with logarithmic nonlinearities, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 23 (1975), no. 4, 461-466.

4.
I. Bialynicki-Birula and J. Mycielski, Nonlinear wave mechanics, Ann. Physics 100 (1976), no. 1-2, 62-93. crossref(new window)

5.
H. Buljan, A. Siber, M. Soljacic, T. Schwartz, M. Segev, and D. N. Christodoulides, Incoherent white light solitons in logarithmically saturable noninstantaneous nonlinear media, Phys. Rev. E (3) 68 (2003), no. 3, 036607, 6 pp. crossref(new window)

6.
T. Cazenave, Stable solutions of the logarithmic Schrodinger equation, Nonlinear Anal. 7 (1983), 1127-1140. crossref(new window)

7.
T. Cazenave and A. Haraux, Equations d'evolution avec non-linearite logarithmique, Ann. Fac. Sci. Toulouse Math. (5) 2 (1980), no. 1, 21-51. crossref(new window)

8.
T. Cazenave and A. Haraux, Equation de Schrodinger avec non-linearite logarithmique, C. R. Acad. Sci. Paris Ser. A-B 288 (1979), no. 4, A253-A256.

9.
S. De Martino, M. Falanga, C. Godano, and G. Lauro, Logarithmic Schr¨odinger-like equation as a model for magma transport, Europhys. Lett. 63 (2003), no. 3, 472-475. crossref(new window)

10.
K. Enqvist and J. McDonald, Q-balls and baryogenesis in the MSSM, Phys. Lett. B 425 (1998), 309-321. crossref(new window)

11.
Y. Giga, S. Matsuiy, and O. Sawada, Global existence of two-dimensional Navier-Stokes flow with nondecaying initial velocity, J. Math. Fuid Mech. 3 (2001), no. 3, 302-315. crossref(new window)

12.
P. Gorka, Logarithmic Klein-Gordon equation, Acta Phys. Polon. B 40 (2009), no. 1, 59-66.

13.
P. Gorka, Logarithmic quantum mechanics: existence of the ground state, Found. Phys. Lett. 19 (2006), no. 6, 591-601. crossref(new window)

14.
P. Gorka, Convergence of logarithmic quantum mechanics to the linear one, Lett. Math. Phys. 81 (2007), no. 3, 253-264. crossref(new window)

15.
P. Gorka, H. Prado, and E. G. Reyes, Functional calculus via Laplace transform and equations with infinitely many derivatives, J. Math. Phys. 51 (2010), no. 10, 103512, 10 pp. crossref(new window)

16.
P. Gorka, H. Prado, and E. G. Reyes, Nonlinear equations with infinitely many derivatives, Complex Anal. Oper. Theory 5 (2011), no. 1, 313-323. crossref(new window)

17.
L. Gross, Logarithmic Sobolev inequalities, Amer. J. Math. 97 (1975), no. 4, 1061-1083. crossref(new window)

18.
T. Hiramatsu, M. Kawasaki, and F. Takahashi, Numerical study of Q-ball formation in gravity mediation, Journal of Cosmology and Astroparticle Physics 2010 (2010), no. 6, 008.

19.
W. Krolikowski, D. Edmundson, and O. Bang, Unified model for partially coherent solitons in logarithmically nonlinear media, Phys. Rev. E 61 (2000), 3122-3126. crossref(new window)

20.
A. Linde, Strings, textures, inflation and spectrum bending, Phys. Lett. B 284 (1992), 215-222. crossref(new window)

21.
V. S. Vladimirov, The equation of the p-adic open string for the scalar tachyon field, Izv. Math. 69 (2005), no. 3, 487-512. crossref(new window)

22.
V. S. Vladimirov and Ya. I. Volovich, Nonlinear dynamics equation in p-adic string theory, Teoret. Mat. Fiz. 138 (2004), 355-368. crossref(new window)

23.
S. Zheng, Nonlinear Evolution Equations, Chapman & Hall/CRC, Boca Raton, FL, 2004.