Initial boundary value problem for p-Laplacian type parabolic equation with singular potential and logarithmic nonlinearity
Tóm tắt
Từ khóa
Tài liệu tham khảo
Buljan, H., Siber, A., Soljacic, M., Schwartz, T., Segev, M., Christodoulides, D.N.: Incoherent white light solitons in logarithmically saturable noninstantaneous nonlinear media. Phys. Rev. E. 68, 6 (2003)
Chen, P.J., Gurtin, M.E.: On a theory of heat conduction involving two temperatures. Z. Angew. Math. Phys. 19, 614–627 (1968)
Han, X.S.: Global existence of weak solutions for a logarithmic wave equation arising from Q-balldynamics. Bull. Korean Math. Soc. 50, 275–283 (2013)
Boulaaras, S., Draifia, A., Alnegga, M.: Polynomial decay rate for Kirchhoff type in viscoelasticity with logarithmic nonlinearity and not necessarily decreasing kernel. Symmetry 11, 1–24 (2019)
Górka, P.: Logarithmic Klein–Gordon equation. Acta Phys. Pol. B 40, 59–66 (2009)
Vittorino, P., Sergey, Z.: Smooth attractors for strongly damped wave equations. Nonlinearity 19, 1495–1506 (2006)
Di, H.F., Shang, Y.D., Song, Z.F.: Initial boundary value problem for a class of strongly damped semilinear wave equations with logarithmic nonlinearity. Nonlinear Anal. Real World Appl. 51, 22 (2020)
Chen, H., Tian, S.Y.: Initial boundary value problem for a class of semilinear pseudo-parabolic equations with logarithmic nonlinearity. J. Differ. Equ. 258, 4424–4442 (2015)
Han, Y.Z., Li, Q.: Lifespan of solutions to a damped plate equation with logarithmic nonlinearity. Evol. Equ. Control Theory 11, 25–40 (2022)
Lian, W., Xu, R.Z.: Global well-posedness of nonlinear wave equation with weak and strong damping terms and logarithmic source term. Adv. Nonlinear Anal. 9, 613–632 (2020)
Ma, L.W., Fang, Z.B.: Energy decay estimates and infinite blow-up phenomena for a strongly damped semilinear wave equation with logarithmic nonlinear source. Math. Methods Appl. Sci. 41, 2639–2653 (2018)
Zu, G., Guo, B.: Bounds for lifespan of solutions to strongly damped semilinear wave equations with logarithmic sources and arbitrary initial energy. Evol. Equ. Control Theory 10, 259–270 (2021)
Xie, M.H., Tan, Z., Wu, Z.E.: Local existence and uniqueness of weak solutions to fractional pseudo-parabolic equation with singular potential. Appl. Math. Lett. 114, 9 (2021)
Hang, D., Zhou, J.: Global existence and blow-up for a mixed pseudo-parabolic $$p$$-Laplacian type equation with logarithmic nonlinearity. J. Math. Anal. Appl. 478, 393–420 (2019)
Le, C.N., Truong, L.X.: Global solution and blow-up for a class of pseudo $$p$$-Laplacian evolution equations with logarithmic nonlinearity. Comput. Math. Appl. 73, 2076–2091 (2017)
He, Y.J., Gao, H.H., Wang, H.: Blow-up and decay for a class of pseudo-parabolic $$p$$-Laplacian equation with logarithmic nonlinearity. Comput. Math. Appl. 75, 459–469 (2018)
Dai, P., Mu, C.L., Xu, G.Y.: Blow-up phenomena for a pseudo-parabolic equation with $$p$$-Laplacian and logarithmic nonlinearity terms. J. Math. Anal. Appl. 481, 27 (2020)
Xu, R.Z., Su, J.: Global existence and finite time blow-up for a class of semilinear pseudo-parabolic equations. J. Funct. Anal. 264, 2732–2763 (2013)
Bisci, G.M., Radulescu, V.D., Servadei, R.: Variational Methods for Nonlocal Fractional Problems. Encyclopedia of Mathematics and Its Applications. Cambridge University Press, Cambridge (2016)
Deng, X.M., Zhou, J.: Global existence and blow-up of solutions to a semilinear heat equation with singular potential and logarithmic nonlinearity. Commun. Pure Appl. Anal. 19, 923–939 (2020)
Lian, W., Wang, J., Xu, R.Z.: Global existence and blow up of solutions for pseudo-parabolic equation with singular potential. J. Differ. Equ. 269, 4914–4959 (2020)
Badiale, M., Tarantello, G.: A Sobolev-Hardy inequality with applications to a nonlinear elliptic equation arising in astrophysics. Arch. Ration. Mech. Anal. 163, 259–293 (2002)
Zheng, S.: Nonlinear Evolution Equations. CRC Press, Boca Raton (2004)