본문 바로가기
KERD
논문KCI 등재

Blow-up and global solutions for some parabolic systems under nonlinear boundary conditions

Limin Guo|Lishan Liu|Yonghong Wu|Yu-mei Zou
대한수학회 (The Korean Mathematical Society)|2019.07|대한수학회지 (Journal of the KMS)|제56권 제4호|pp. 1017-1029|DOI 10.4134/JKMS.j180539

1

조회

0

다운로드

0

인용

0

참고문헌

키워드

nonlinear boundary conditionsparabolic equationsblows-up and global solutionstime dependent coefficientsabstract form of $(\varrho(u))_{t}$
주제분류수학

초록

In this paper, blows-up and global solutions for a class of nonlinear divergence form parabolic equations with the abstract form of $(\varrho(u))_{t}$ and time dependent coefficients are considered. The conditions are established for the existence of a solution globally and also the conditions are established for the blow up of the solution at some finite time. Moreover, the lower bound and upper bound of the blow-up time are derived if blow-up occurs.

Abstract

In this paper, blows-up and global solutions for a class of nonlinear divergence form parabolic equations with the abstract form of $(\varrho(u))_{t}$ and time dependent coefficients are considered. The conditions are established for the existence of a solution globally and also the conditions are established for the blow up of the solution at some finite time. Moreover, the lower bound and upper bound of the blow-up time are derived if blow-up occurs.

참고문헌 (21)

  1. J. M. Arrieta, "Parabolic problems with nonlinear boundary conditions and critical nonlinearities", J. Differential Equations, 156(2), pp.376~406 (1999)
  2. J. Ding, "Blow-up and global solutions for a class of nonlinear reaction diffusion equations under Dirichlet boundary conditions", J. Math. Anal. Appl, 433(2), pp.1718~1735 (2016)
  3. C. Enache, "Lower bounds for blow-up time in some non-linear parabolic problems under Neumann boundary conditions", Glasg. Math. J, 53(3), pp.569~575 (2011)
  4. Z. B. Fang, "Blow-up analysis for a semilinear parabolic equation with time-dependent coefficients under nonlinear boundary flux", Z. Angew. Math. Phys, 66(5), pp.2525~2541 (2015)
  5. F. Li, "Global existence and blow-up phenomena for nonlinear divergence form parabolic equations with inhomogeneous Neumann boundary conditions", J. Math. Anal. Appl, 385(2), pp.1005~1014 (2012)
  6. F. Li, "Multiple solutions to a class of generalized quasilinear Schr¨odinger equations with a Kirchhoff-type perturbation", J. Math. Anal. Appl, 443(1), pp.11~38 (2016)
  7. D. Liu, "Lower bounds estimate for the blow-up time of a nonlinear nonlocal porous medium equation", Acta Math. Sci. Ser. B (Engl. Ed.), 32(3), pp.1206~1212 (2012)
  8. L. E. Payne, "Blow-up in a class of non-linear parabolic problems with time-dependent coefficients under Robin type boundary conditions", Appl. Anal, 91(12), pp.2245~2256 (2012)
  9. L. E. Payne, "Bounds for blow-up time in nonlinear parabolic problems", J. Math. Anal. Appl, 338(1), pp.438~447 (2008)
  10. L. E. Payne, "Lower bounds for blow-up time in parabolic problems under Neumann conditions", Appl. Anal, 85(10), pp.1301~1311 (2006)
  11. L. E. Payne, "Bounds for blow-up time for the heat equation under nonlinear boundary conditions", Proc. Roy. Soc. Edinburgh Sect. A, 139(6), pp.1289~1296 (2009)
  12. L. E. Payne, "Blow-up and decay criteria for a model of chemotaxis", J. Math. Anal. Appl, 367(1), pp.1~6 (2010)
  13. L. E. Payne, "Lower bounds for blow-up in a model of chemotaxis", J. Math. Anal. Appl, 385(2), pp.672~676 (2012)
  14. X. Song, "Bounds for the blowup time and blowup rate estimates for a type of parabolic equations with weighted source", Appl. Math. Comput, 236, pp.78~92 (2014)
  15. P. Souplet, "Blow-up in nonlocal reaction-diffusion equations", SIAM J. Math. Anal, 29(6), pp.1301~1334 (1998)
  16. F. Sun, "Infinitely many sign-changing solutions for a class of biharmonic equation with p-Laplacian and Neumann boundary condition", Appl. Math. Lett, 73, pp.128~135 (2017)
  17. Fenglong Sun, "Blow-up of solutions for a nonlinear viscoelastic wave equation with initial data at arbitrary energy level", Applicable Analysis, 98(12), pp.2308~2327 (2018), Informa UK Limited[DOI]
  18. F. Sun, "Finite time blow-up for a thin-film equation with initial data at arbitrary energy level", J. Math. Anal. Appl, 458(1), pp.9~20 (2018)
  19. F. Sun, "Finite time blow-up for a class of parabolic or pseudo-parabolic equations", Com-put. Math. Appl, 75(10), pp.3685~3701 (2018)
  20. F. Sun, "Global existence and finite time blow-up of solutions for the semilinear pseudoparabolic equation with a memory term", Appl. Anal, 98(4), pp.735~755 (2019)
  21. X. Yang, "Blow-up problems for the heat equation with a local nonlinear Neumann boundary condition", J. Differential Equations, 261(5), pp.2738~2783 (2016)

관련 논문AI추천

A PARABOLIC SYSTEM WITH NONLOCAL BOUNDARY CONDITIONS AND NONLOCAL SOURCESWenjie Gao, Yuzhu Han대한수학회 · 대한수학회논문집2012 · 제27권 제3호Global existence and blow-up for a degenerate reaction-diffusion system with nonlinear localized sources and nonlocal boundary conditionsFei Liang대한수학회 · 대한수학회지2016 · 제53권 제1호Some types of reaction-diffusion systems with nonlocal boundary conditionsWenjie Gao, Yuzhu Han대한수학회 · 대한수학회보2013 · 제50권 제6호CRITICAL EXPONENTS FOR A DOUBLY DEGENERATE PARABOLIC SYSTEM COUPLED VIA NONLINEAR BOUNDARY FLUXBotao Chen, Chunlai Mu, Yongsheng Mi대한수학회 · 대한수학회지2011 · 제48권 제3호Local and global existence and blow-up of solutions to a polytropic filtration system with nonlinear memory and nonlinear boundary conditionsJian Wang, Meng-long Su, Zhong Bo Fang대한수학회 · 대한수학회보2013 · 제50권 제1호Blow-up time and blow-up rate for pseudo-parabolic equations with weighted sourceHuafei Di, Yadong Shang대한수학회 · 대한수학회논문집2020 · 제35권 제4호

이 간행물의 다른 논문 (13건)

On a class of quasilinear elliptic equation with indefinite weights on graphsGuoqing Zhang, Shoudong Manpp. 857-867A characterization of class groups via sets of lengthsAlfred Geroldinger, Wolfgang Alexander Schmidpp. 869-915Homogeneity and symmetry on almost Kenmotsu $3$-manifoldsYaning Wangpp. 917-934Limit theorems for Hawkes processes with uniform immigrants설영수pp. 935-946Shifted tableau switchings and shifted Littlewood-Richardson coefficients최승일, 오영탁, 남선영pp. 947-984
원문 보기