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Volumn 46, Issue 3-4, 2006, Pages 325-347

Global behavior of solutions of a reaction-diffusion equation with gradient absorption in unbounded domains

Author keywords

Finite time blow up; Global existence; Gradient term; Inradius; Nonlinear parabolic equations; Poincar inequality

Indexed keywords

BOUNDARY CONDITIONS; MATHEMATICAL MODELS; PROBLEM SOLVING;

EID: 33644600185     PISSN: 09217134     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (44)

References (29)
  • 1
    • 0011523442 scopus 로고
    • N for a parabolic equation with a damping nonlinear gradient term
    • N.G. Lloyd et al. (eds), Birkhäuser, Boston
    • N for a parabolic equation with a damping nonlinear gradient term, in: N.G. Lloyd et al. (eds), Diffusion Equations and Their Equilibrium States, III, Birkhäuser, Boston, 1992, pp. 1-10.
    • (1992) Diffusion Equations and Their Equilibrium States, III , pp. 1-10
    • Alfonsi, L.1    Weissler, F.B.2
  • 2
    • 0033454325 scopus 로고    scopus 로고
    • Global existence for a degenerate nonlinear diffusion problem with nonlinear gradient term and source
    • F. Andreu, J.M. Mazon, F. Simondon and J. Toledo, Global existence for a degenerate nonlinear diffusion problem with nonlinear gradient term and source, Math. Am. 314 (1999), 703-728.
    • (1999) Math. Am. , vol.314 , pp. 703-728
    • Andreu, F.1    Mazon, J.M.2    Simondon, F.3    Toledo, J.4
  • 3
    • 1642367710 scopus 로고    scopus 로고
    • Gradient bounds for solutions of semilinear parabolic equations without Bernstein's quadratic condition
    • J.Ph. Bartier and Ph. Souplet, Gradient bounds for solutions of semilinear parabolic equations without Bernstein's quadratic condition, C. R. Acad. Sci. Paris 338(7) (2004), 533-538.
    • (2004) C. R. Acad. Sci. Paris , vol.338 , Issue.7 , pp. 533-538
    • Bartier, J.Ph.1    Souplet, Ph.2
  • 4
    • 0003255150 scopus 로고    scopus 로고
    • An introduction to semilinear evolution equations
    • The Clarendon Press, Oxford University Press, New York
    • T. Cazenave and A. Haraux, An Introduction to Semilinear Evolution Equations, Oxford Lecture Series in Mathematics and its Applications, Vol. 13, The Clarendon Press, Oxford University Press, New York, 1998. xiv+186 pp.
    • (1998) Oxford Lecture Series in Mathematics and Its Applications , vol.13
    • Cazenave, T.1    Haraux, A.2
  • 5
    • 0000581856 scopus 로고
    • Some blow up results for a nonlinear parabolic problem with a gradient term
    • M. Chipot and F.B. Weissler, Some blow up results for a nonlinear parabolic problem with a gradient term, SIAM J. Math. Anal. 20 (1989), 886-907.
    • (1989) SIAM J. Math. Anal. , vol.20 , pp. 886-907
    • Chipot, M.1    Weissler, F.B.2
  • 6
    • 0002499851 scopus 로고    scopus 로고
    • From critical exponents to blowup rates for parabolic problems
    • M. Chlebik and M. Fila, From critical exponents to blowup rates for parabolic problems, Rend. Mat. Appl. Ser. VII 19 (1999), 449-470.
    • (1999) Rend. Mat. Appl. Ser. VII , vol.19 , pp. 449-470
    • Chlebik, M.1    Fila, M.2
  • 7
    • 84894265109 scopus 로고    scopus 로고
    • Blowup of positive solutions of a semilinear parabolic equation with a gradient term
    • to appear
    • M. Chlebik, M. Fila and P. Quittner, Blowup of positive solutions of a semilinear parabolic equation with a gradient term, Dyn. Contin. Discrete Impulsive Syst., to appear.
    • Dyn. Contin. Discrete Impulsive Syst.
    • Chlebik, M.1    Fila, M.2    Quittner, P.3
  • 8
    • 51249168390 scopus 로고
    • Stabilization of solutions of a nonlinear parabolic equation with a gradient term
    • K. Deng, Stabilization of solutions of a nonlinear parabolic equation with a gradient term, Math. Z. 216 (1994), 147-155.
    • (1994) Math. Z. , vol.216 , pp. 147-155
    • Deng, K.1
  • 9
    • 84968503362 scopus 로고
    • Remarks on blow up for a nonlinear parabolic equation with a gradient term
    • M. Fila, Remarks on blow up for a nonlinear parabolic equation with a gradient term, Proc. Amer. Math. Soc. 111 (1991), 795-801.
    • (1991) Proc. Amer. Math. Soc. , vol.111 , pp. 795-801
    • Fila, M.1
  • 10
    • 0038563718 scopus 로고    scopus 로고
    • The blowup rate for semilinear parabolic problems on general domains
    • M. Fila and Ph. Souplet, The blowup rate for semilinear parabolic problems on general domains, NoDEA 8 (2001), 473-180.
    • (2001) NoDEA , vol.8 , pp. 473-1180
    • Fila, M.1    Souplet, Ph.2
  • 11
    • 0000885478 scopus 로고
    • Observations on blowup and dead cores for nonlinear parabolic equations
    • B. Kawohl and L. Peletier, Observations on blowup and dead cores for nonlinear parabolic equations, Math. Z. 202 (1989), 207-217.
    • (1989) Math. Z. , vol.202 , pp. 207-217
    • Kawohl, B.1    Peletier, L.2
  • 12
    • 0001156676 scopus 로고
    • Linear and quasi-linear equations of parabolic type
    • Translations of Mathematical Monographs, Providence, RI
    • O.A. Ladyzhenskaja, V.A. Solonnikov and N.N. Ural'ceva, Linear and Quasi-linear Equations of Parabolic Type, Translations of Mathematical Monographs, Vol. 23, Amer. Math. Soc., Providence, RI, 1967.
    • (1967) Amer. Math. Soc. , vol.23
    • Ladyzhenskaja, O.A.1    Solonnikov, V.A.2    Ural'Ceva, N.N.3
  • 14
    • 84988169902 scopus 로고
    • Blowup for semilinear parabolic equations with a gradient term
    • P. Quittner, Blowup for semilinear parabolic equations with a gradient term, Math. Methods Appl. Sci. 14 (1991), 413-417.
    • (1991) Math. Methods Appl. Sci. , vol.14 , pp. 413-417
    • Quittner, P.1
  • 15
    • 0001259529 scopus 로고
    • On global existence and stationary solutions for two classes of semilinear parabolic equations
    • P. Quittner, On global existence and stationary solutions for two classes of semilinear parabolic equations, Comment. Math. Univ. Carolin. 34 (1993), 105-124.
    • (1993) Comment. Math. Univ. Carolin. , vol.34 , pp. 105-124
    • Quittner, P.1
  • 16
    • 0038784323 scopus 로고    scopus 로고
    • A priori estimates of global solutions of superlinear parabolic problems without variational structure
    • P. Quittner and Ph. Souplet, A priori estimates of global solutions of superlinear parabolic problems without variational structure, Discrete Continuous Dynamical Systems 9 (2003), 1277-1292.
    • (2003) Discrete Continuous Dynamical Systems , vol.9 , pp. 1277-1292
    • Quittner, P.1    Souplet, Ph.2
  • 17
    • 0035541513 scopus 로고    scopus 로고
    • Blowup of solutions of nonlinear heat equations in unbounded domains for slowly decaying initial data
    • P. Rouchon, Blowup of solutions of nonlinear heat equations in unbounded domains for slowly decaying initial data, Z Angew. Math. Phys. 52 (2001), 1017-1032.
    • (2001) Z Angew. Math. Phys. , vol.52 , pp. 1017-1032
    • Rouchon, P.1
  • 18
    • 21144481357 scopus 로고
    • Existence and non-existence for ground states of quasilinear elliptic equations
    • J. Serrin and H. Zou, Existence and non-existence for ground states of quasilinear elliptic equations, Arch. Rational Mech. Anal. 121 (1992), 101-130.
    • (1992) Arch. Rational Mech. Anal. , vol.121 , pp. 101-130
    • Serrin, J.1    Zou, H.2
  • 19
    • 22844454513 scopus 로고    scopus 로고
    • Asymptotically self-similar global solutions of a semilinear parabolic equation with a nonlinear gradient terms
    • S. Snoussi, S. Tayachi and F.B. Weissler, Asymptotically self-similar global solutions of a semilinear parabolic equation with a nonlinear gradient terms, Proc. Roy. Soc. Edinburgh A 129 (1999), 1291-1307.
    • (1999) Proc. Roy. Soc. Edinburgh A , vol.129 , pp. 1291-1307
    • Snoussi, S.1    Tayachi, S.2    Weissler, F.B.3
  • 20
    • 0030282583 scopus 로고    scopus 로고
    • Finite time blow-up for a non-linear parabolic equation with a gradient term and Applications
    • Ph. Souplet, Finite time blow-up for a non-linear parabolic equation with a gradient term and Applications, Math. Methods Appl. Sci. 19 (1996), 1317-1333.
    • (1996) Math. Methods Appl. Sci. , vol.19 , pp. 1317-1333
    • Souplet, Ph.1
  • 21
    • 0033474488 scopus 로고    scopus 로고
    • Geometry of unbounded domains, Poincaré inequalities, and stability in semilinear parabolic equations
    • Ph. Souplet, Geometry of unbounded domains, Poincaré inequalities, and stability in semilinear parabolic equations, Comm. Partial Differential Equations 24 (1999), 951-973.
    • (1999) Comm. Partial Differential Equations , vol.24 , pp. 951-973
    • Souplet, Ph.1
  • 22
    • 0005794876 scopus 로고    scopus 로고
    • Recent results and open problems on parabolic equations with gradient nonlinearities
    • Ph. Souplet, Recent results and open problems on parabolic equations with gradient nonlinearities, Electronic J. Differential Equations 10 (2001), 1-19.
    • (2001) Electronic J. Differential Equations , vol.10 , pp. 1-19
    • Souplet, Ph.1
  • 23
    • 0347340615 scopus 로고    scopus 로고
    • Blowup rates for nonlinear heat equations with gradient terms and for parabolic inequalities
    • Ph. Souplet and S. Tayachi, Blowup rates for nonlinear heat equations with gradient terms and for parabolic inequalities, Colloq. Math. 88 (2001), 135-154.
    • (2001) Colloq. Math. , vol.88 , pp. 135-154
    • Souplet, Ph.1    Tayachi, S.2
  • 24
    • 0000126964 scopus 로고    scopus 로고
    • Exact self-similar blowup of solutions of a semilinear parabolic equation with a nonlinear gradient term
    • Ph. Souplet, S. Tayachi and F.B. Weissler, Exact self-similar blowup of solutions of a semilinear parabolic equation with a nonlinear gradient term, Indiana Univ. Math. J. 45 (1996), 655-682.
    • (1996) Indiana Univ. Math. J. , vol.45 , pp. 655-682
    • Souplet, Ph.1    Tayachi, S.2    Weissler, F.B.3
  • 25
    • 0031195373 scopus 로고    scopus 로고
    • Self-similar subsolutions and blowup for nonlinear parabolic equations
    • Ph. Souplet and F. Weissler, Self-similar subsolutions and blowup for nonlinear parabolic equations, J. Math. Anal. Appl. 212 (1997), 60-74.
    • (1997) J. Math. Anal. Appl. , vol.212 , pp. 60-74
    • Souplet, Ph.1    Weissler, F.2
  • 26
    • 0012103230 scopus 로고    scopus 로고
    • Poincaré's inequality and global solutions of a nonlinear parabolic equation
    • Ph. Souplet and F. Weissler, Poincaré's inequality and global solutions of a nonlinear parabolic equation, Ann. Inst. H. Poincaré Anal. Non Linéaire 16 (1999), 335-371.
    • (1999) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.16 , pp. 335-371
    • Souplet, Ph.1    Weissler, F.2
  • 27
    • 0000804641 scopus 로고    scopus 로고
    • Forward self-similar solutions of a semilinear parabolic equation with a nonlinear gradient term
    • S. Tayachi, Forward self-similar solutions of a semilinear parabolic equation with a nonlinear gradient term, Differential Integral Equations 9 (1996), 1107-1117.
    • (1996) Differential Integral Equations , vol.9 , pp. 1107-1117
    • Tayachi, S.1
  • 28
    • 2942581085 scopus 로고    scopus 로고
    • The preventive effect of the convection and of the diffusion in the blow-up phenomenon for parabolic equations
    • Al. Tersenov, The preventive effect of the convection and of the diffusion in the blow-up phenomenon for parabolic equations, Ann. Inst. H. Poincaré 4 (2004), 533-541.
    • (2004) Ann. Inst. H. Poincaré , vol.4 , pp. 533-541
    • Tersenov, Al.1
  • 29
    • 0010959930 scopus 로고    scopus 로고
    • Coexistence of singular and regular solutions for the equation of Chipot and Weissler
    • F. Voirol, Coexistence of singular and regular solutions for the equation of Chipot and Weissler, Acta Math. Univ. Comenian. 65 (1996), 53-64.
    • (1996) Acta Math. Univ. Comenian. , vol.65 , pp. 53-64
    • Voirol, F.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.