메뉴 건너뛰기




Volumn 27, Issue 1, 1998, Pages 147-196

Existence and nonexistence of global solutions to quasilinear parabolic equations with convection

Author keywords

Asymptotic behavior; Blow up; Cauchy problem; Convection; Critical exponent; Global solution; L Ll estimate; Quasilinear parabolic equation

Indexed keywords


EID: 0001572425     PISSN: 03854035     EISSN: None     Source Type: Journal    
DOI: 10.14492/hokmj/1351001256     Document Type: Article
Times cited : (22)

References (30)
  • 1
    • 84971116414 scopus 로고
    • On the blow-up of solutions of a convective reaction diffusion equation
    • Aguirre J. and Escobedo M., On the blow-up of solutions of a convective reaction diffusion equation. Proc. Royal Soc. Edinburgh 123A (1993), 433-460.
    • (1993) Proc. Royal Soc. Edinburgh , vol.123A , pp. 433-460
    • Aguirre, J.1    Escobedo, M.2
  • 2
    • 0001483956 scopus 로고
    • Stabilization of solutions of a degenerate nonlinear diffusion problem
    • Aronson D.G., Crandall M.G. and Peletier L.A., Stabilization of solutions of a degenerate nonlinear diffusion problem. Nonlinear Anal. 6 (1982), 1001-1022.
    • (1982) Nonlinear Anal , vol.6 , pp. 1001-1022
    • Aronson, D.G.1    Crandall, M.G.2    Peletier, L.A.3
  • 3
    • 0000701823 scopus 로고
    • Positivity versus localization in degenerate diffusion equations
    • Bertsch M., Kersner R. and Peletier L.A., Positivity versus localization in degenerate diffusion equations. Nonlinear Anal. 9 (1985), 987-1008.
    • (1985) Nonlinear Anal , vol.9 , pp. 987-1008
    • Bertsch, M.1    Kersner, R.2    Peletier, L.A.3
  • 4
    • 0002449197 scopus 로고
    • Continuity of weak solutions to a general porous medium equation
    • DiBenedetto E., Continuity of weak solutions to a general porous medium equation. Indiana Univ. Math. J. 32 (1983), 83-118.
    • (1983) Indiana Univ. Math. J , vol.32 , pp. 83-118
    • Dibenedetto, E.1
  • 5
    • 0000021267 scopus 로고
    • A diffusion-convection equation in several space dimensions
    • Escobedo M., Vázquez J.L. and Zuazua E., A diffusion-convection equation in several space dimensions. Indiana Univ. Math. J. 42 (1993), 1413-1440.
    • (1993) Indiana Univ. Math. J , vol.42 , pp. 1413-1440
    • Escobedo, M.1    Vázquez, J.L.2    Zuazua, E.3
  • 6
  • 7
    • 84968502599 scopus 로고
    • The asymptotic behavior of gas in a n-dimensional porous medium
    • Friedman A. and Kamin S., The asymptotic behavior of gas in a n-dimensional porous medium. Trans. Amer. Math. Soc. 262 (1980), 551-563.
    • (1980) Trans. Amer. Math. Soc , vol.262 , pp. 551-563
    • Friedman, A.1    Kamin, S.2
  • 8
    • 38249028960 scopus 로고
    • Blowup of solutions of semilinear parabolic equations
    • Friedman A. and Lacey A.A., Blowup of solutions of semilinear parabolic equations. J. Math. Anal. Appl. 132 (1988), 171-186.
    • (1988) J. Math. Anal. Appl , vol.132 , pp. 171-186
    • Friedman, A.1    Lacey, A.A.2
  • 10
    • 84973976169 scopus 로고
    • Blow-up for quasilinear heat equations with critical Fujita’s exponents
    • Galaktionov V.A., Blow-up for quasilinear heat equations with critical Fujita’s exponents. Proc. Roy. Soc. Edinburgh 124A (1994), 517-525.
    • (1994) Proc. Roy. Soc. Edinburgh , vol.124A , pp. 517-525
    • Galaktionov, V.A.1
  • 12
  • 13
    • 0000469761 scopus 로고
    • On nonexistence of global solutions of some semilinear parabolic equations
    • Hayakawa K., On nonexistence of global solutions of some semilinear parabolic equations. Proc. Japan Acad. 49 (1973), 503-505.
    • (1973) Proc. Japan Acad , vol.49 , pp. 503-505
    • Hayakawa, K.1
  • 14
    • 84966253246 scopus 로고
    • Singular limit of solutions of ut = ∇um − A ∇(Uq/q) as q → ∞
    • q/q) as q → ∞. Trans. Amer. Math. Soc. 347 (1991), 1687-1712.
    • (1991) Trans. Amer. Math. Soc , vol.347 , pp. 1687-1712
    • Hui, K.M.1
  • 15
    • 85008550406 scopus 로고
    • On blow-up of solutions for quasilinear degenerate parabolic equations
    • Kyoto Univ
    • Imai T. and Mochizuki K., On blow-up of solutions for quasilinear degenerate parabolic equations. Publ. RIMS, Kyoto Univ. 27 (1991), 695-709.
    • (1991) Publ. RIMS , vol.27 , pp. 695-709
    • Imai, T.1    Mochizuki, K.2
  • 16
    • 33845786226 scopus 로고
    • On blow-up problems for quasilinear degenerate parabolic equations with convection. Nonlinear Mathematical Problems in Industry, GAKUTO International Series
    • Imai T., Mochizuki K. and Suzuki R., On blow-up problems for quasilinear degenerate parabolic equations with convection. Nonlinear Mathematical Problems in Industry, GAKUTO International Series, Mathematical Sciences and Applications 2 (1993), 435-448.
    • (1993) Mathematical Sciences and Applications , vol.2 , pp. 435-448
    • Imai, T.1    Mochizuki, K.2    Suzuki, R.3
  • 18
    • 84972549957 scopus 로고
    • The behavior of solutions of quasi-linear heat equations
    • Kawanago T., The behavior of solutions of quasi-linear heat equations. Osaka J. Math. 27 (1990), 769-796.
    • (1990) Osaka J. Math , vol.27 , pp. 769-796
    • Kawanago, T.1
  • 20
    • 0025442951 scopus 로고
    • The role of critical exponents in blowup theorems
    • Levine H.A., The role of critical exponents in blowup theorems. SIAM Review 32 (1990), 262-288.
    • (1990) SIAM Review , vol.32 , pp. 262-288
    • Levine, H.A.1
  • 22
    • 84990586468 scopus 로고
    • Asymptotic behavior of the solutions of certain parabolic equations
    • Lortz D., Meyer-Spasche R. and Stredulinsky E.W., Asymptotic behavior of the solutions of certain parabolic equations. Comm. Pure Appl. Math. 37 (1984), 677-703.
    • (1984) Comm. Pure Appl. Math , vol.37 , pp. 677-703
    • Lortz, D.1    Meyer-Spasche, R.2    Stredulinsky, E.W.3
  • 23
    • 0008726515 scopus 로고
    • Existence and nonexistence of global solutions to fast diffusions with source
    • Mochizuki K. and Mukai K., Existence and nonexistence of global solutions to fast diffusions with source. Methods and Applications of Analysis 2 (1995), 92-102.
    • (1995) Methods and Applications of Analysis , vol.2 , pp. 92-102
    • Mochizuki, K.1    Mukai, K.2
  • 24
    • 0000722446 scopus 로고    scopus 로고
    • Critical exponent and critical blow-up for quasilinear parabolic equations
    • Mochizuki K. and Suzuki R., Critical exponent and critical blow-up for quasilinear parabolic equations. Israel J. Math. 98 (1997), 141-156.
    • (1997) Israel J. Math , vol.98 , pp. 141-156
    • Mochizuki, K.1    Suzuki, R.2
  • 25
    • 0039044675 scopus 로고
    • L∞-estimate of solutions of some nonlinear degenerate parabolic equations
    • ∞-estimate of solutions of some nonlinear degenerate parabolic equations. Nonlinear Anal. T.M.A. 18 (1992), 413-426.
    • (1992) Nonlinear Anal. T.M.A. , vol.18 , pp. 413-426
    • Ohara, Y.1
  • 26
    • 0001217997 scopus 로고
    • The Cauchy problem and boundary problems for equations of the type of nonlinear filtration
    • Russian
    • Oleinik O.A., Kalashnikov A.S. and Chzou Yui-Lin, The Cauchy problem and boundary problems for equations of the type of nonlinear filtration. Izv. Akad. Nauk. SSSR Ser. Math. 22 (1958), 667-704, (Russian).
    • (1958) Izv. Akad. Nauk. SSSR Ser. Math , vol.22 , pp. 667-704
    • Oleinik, O.A.1    Kalashnikov, A.S.2    Yui-Lin, C.3
  • 27
    • 0001497003 scopus 로고
    • Uniqueness of the solutions of ut − ∆ψ(U)= 0 with initial datum a measure
    • t − ∆ψ(u)= 0 with initial datum a measure. Nonlinear Anal. T.M.A. 6 (1982), 175-187.
    • (1982) Nonlinear Anal. T.M.A. , vol.6 , pp. 175-187
    • Pierre, M.1
  • 28
    • 74849135510 scopus 로고
    • Blow-up solutions of quasilinear degenerate parabolic equations with convection
    • Suzuki R., Blow-up solutions of quasilinear degenerate parabolic equations with convection. SIAM Math. Anal. 26 (1995), 77-97.
    • (1995) SIAM Math. Anal , vol.26 , pp. 77-97
    • Suzuki, R.1
  • 29
    • 0346166976 scopus 로고    scopus 로고
    • Critical blow-up for quasilinear parabolic equations in exterior domains
    • Tokyo
    • Suzuki R., Critical blow-up for quasilinear parabolic equations in exterior domains. Tokyo J. Math. 19 (1996), 397-409.
    • (1996) J. Math , vol.19 , pp. 397-409
    • Suzuki, R.1
  • 30
    • 51249183619 scopus 로고
    • Existence and nonexistence of global solutions for a semilinear heat equation
    • Weissler F.B., Existence and nonexistence of global solutions for a semilinear heat equation. Israel J. Math. 38 (1981), 29-40.
    • (1981) Israel J. Math , vol.38 , pp. 29-40
    • Weissler, F.B.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.