BLOW-UP AND GLOBAL SOLUTIONS FOR SOME PARABOLIC SYSTEMS UNDER NONLINEAR BOUNDARY CONDITIONS |
Guo, Limin
(School of Mathematical Sciences Qufu Normal University)
Liu, Lishan (School of Mathematical Sciences Qufu Normal University) Wu, Yonghong (Department of Mathematics and Statistics Curtin University) Zou, Yumei (Department of Statistics and Finance Shandong University of Science and Technology) |
1 | J. Ding and H. Hu, Blow-up and global solutions for a class of nonlinear reaction diffusion equations under Dirichlet boundary conditions, J. Math. Anal. Appl. 433 (2016), no. 2, 1718-1735. DOI |
2 | C. Enache, Lower bounds for blow-up time in some non-linear parabolic problems under Neumann boundary conditions, Glasg. Math. J. 53 (2011), no. 3, 569-575. DOI |
3 | Z. B. Fang and Y. Wang, Blow-up analysis for a semilinear parabolic equation with time-dependent coefficients under nonlinear boundary flux, Z. Angew. Math. Phys. 66 (2015), no. 5, 2525-2541. DOI |
4 | F. Li and J. Li, Global existence and blow-up phenomena for nonlinear divergence form parabolic equations with inhomogeneous Neumann boundary conditions, J. Math. Anal. Appl. 385 (2012), no. 2, 1005-1014. DOI |
5 | F. Li, X. Zhu and Z. Liang, Multiple solutions to a class of generalized quasilinear Schrodinger equations with a Kirchhoff-type perturbation, J. Math. Anal. Appl. 443 (2016), no. 1, 11-38. DOI |
6 | D. Liu, C. Mu, and Q. Xin, Lower bounds estimate for the blow-up time of a nonlinear nonlocal porous medium equation, Acta Math. Sci. Ser. B (Engl. Ed.) 32 (2012), no. 3, 1206-1212. |
7 | L. E. Payne and G. A. Philippin, Blow-up in a class of non-linear parabolic problems with time-dependent coefficients under Robin type boundary conditions, Appl. Anal. 91 (2012), no. 12, 2245-2256. DOI |
8 | L. E. Payne, G. A. Philippin, and P. W. Schaefer, Bounds for blow-up time in nonlinear parabolic problems, J. Math. Anal. Appl. 338 (2008), no. 1, 438-447. DOI |
9 | J. M. Arrieta, A. N. Carvalho, and A. Rodriguez-Bernal, Parabolic problems with nonlinear boundary conditions and critical nonlinearities, J. Differential Equations 156 (1999), no. 2, 376-406. DOI |
10 | L. E. Payne and P. W. Schaefer, Lower bounds for blow-up time in parabolic problems under Neumann conditions, Appl. Anal. 85 (2006), no. 10, 1301-1311. |
11 | X. Song and X. Lv, Bounds for the blowup time and blowup rate estimates for a type of parabolic equations with weighted source, Appl. Math. Comput. 236 (2014), 78-92. DOI |
12 | L. E. Payne and P. W. Schaefer, Bounds for blow-up time for the heat equation under nonlinear boundary conditions, Proc. Roy. Soc. Edinburgh Sect. A 139 (2009), no. 6, 1289-1296. DOI |
13 | L. E. Payne and J. C. Song, Blow-up and decay criteria for a model of chemotaxis, J. Math. Anal. Appl. 367 (2010), no. 1, 1-6. DOI |
14 | L. E. Payne and J. C. Song, Lower bounds for blow-up in a model of chemotaxis, J. Math. Anal. Appl. 385 (2012), no. 2, 672-676. DOI |
15 | P. Souplet, Blow-up in nonlocal reaction-diffusion equations, SIAM J. Math. Anal. 29 (1998), no. 6, 1301-1334. DOI |
16 | F. Sun, L. Liu, and Y. Wu, Finite time blow-up for a class of parabolic or pseudo-parabolic equations, Comput. Math. Appl. 75 (2018), no. 10, 3685-3701. DOI |
17 | F. Sun, L. Liu, and Y. Wu, Infinitely many sign-changing solutions for a class of biharmonic equation with p-Laplacian and Neumann boundary condition, Appl. Math. Lett. 73 (2017), 128-135. DOI |
18 | F. Sun, L. Liu, and Y. Wu, Blow-up of a nonlinear viscoelastic wave equation with initial data at arbitrary high energy level, Appl. Anal.; DOI: 10.1080/00036811.2018.1460812. |
19 | F. Sun, L. Liu, and Y. Wu, Finite time blow-up for a thin-film equation with initial data at arbitrary energy level, J. Math. Anal. Appl. 458 (2018), no. 1, 9-20. DOI |
20 | F. Sun, L. Liu, and Y. Wu, Global existence and finite time blow-up of solutions for the semilinear pseudoparabolic equation with a memory term, Appl. Anal. 98 (2019), no. 4, 735-755. DOI |
21 | X. Yang and Z. Zhou, Blow-up problems for the heat equation with a local nonlinear Neumann boundary condition, J. Differential Equations 261 (2016), no. 5, 2738-2783. DOI |