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Volumn 66, Issue 3-4, 1997, Pages 291-321

A critical parabolic estimate and application to nonlocal equations arising in chemotaxis

Author keywords

Blow up; Chemotaxis; Parabolic equations

Indexed keywords


EID: 0000646419     PISSN: 15226514     EISSN: 15497879     Source Type: Journal    
DOI: 10.1080/00036819708840588     Document Type: Article
Times cited : (36)

References (22)
  • 1
    • 0002401281 scopus 로고
    • Comparison results for elliptic and parabolic equations via Schwarz symmetrization
    • Alvino, A., Trombetti, G., and Lions, P. L., 1990. Comparison results for elliptic and parabolic equations via Schwarz symmetrization. Ann. Inst. Henri Poincare, 7: 37-65.
    • (1990) Ann. Inst. Henri Poincare , vol.7 , pp. 37-65
    • Alvino, A.1    Trombetti, G.2    Lions, P.L.3
  • 2
    • 84972514673 scopus 로고
    • Comparison results for elliptic and parabolic equations via symmetrization: A new approach
    • Alvino, A., Lions, P. L., and Trombetti, G., 1991. Comparison results for elliptic and parabolic equations via symmetrization: A new approach. Diff. and Int. Eq, 4: 25-50.
    • (1991) Diff. and Int. Eq , vol.4 , pp. 25-50
    • Alvino, A.1    Lions, P.L.2    Trombetti, G.3
  • 3
    • 51249192128 scopus 로고
    • On Symmetrization in parabolic equations
    • Bandle, C., 1976. On Symmetrization in parabolic equations. J. 'Anal. Math, 30: 98-112.
    • (1976) J. 'Anal. Math , vol.30 , pp. 98-112
    • Bandle, C.1
  • 4
    • 0000531920 scopus 로고
    • Existence and nonexistence of solutions for a model of gravitational interaction of particles I
    • Biler, P., and Nadzieja, T., 1994. Existence and nonexistence of solutions for a model of gravitational interaction of particles I. Coll Math, 66: 319-334.
    • (1994) Coll Math , vol.66 , pp. 319-334
    • Biler, P.1    Nadzieja, T.2
  • 5
    • 0000975661 scopus 로고
    • Existence and nonexistence of solutions for a model of gravitational interaction of particles II
    • Biler, P., Hilhorst, D., and Nadzieja, T., 1994. Existence and nonexistence of solutions for a model of gravitational interaction of particles II. Coll Math, 67: 297-308.
    • (1994) Coll Math , vol.67 , pp. 297-308
    • Biler, P.1    Hilhorst, D.2    Nadzieja, T.3
  • 6
    • 77954784778 scopus 로고
    • Uniform estimates and blow up behavior for solutions of in two dimensions
    • Brezis, H., and Merle, F., 1991. Uniform estimates and blow up behavior for solutions of in two dimensions. Comm. P.D.E, 16: 1223-1253.
    • (1991) Comm. P.D.E , vol.16 , pp. 1223-1253
    • Brezis, H.1    Merle, F.2
  • 7
    • 21144473294 scopus 로고
    • Apriori estimates for solutions to nonlinear elliptic equations
    • Chen, W., and Li, C., 1993. Apriori estimates for solutions to nonlinear elliptic equations. Arch. Rat. Mech. Anal, 122: 145-157.
    • (1993) Arch. Rat. Mech. Anal , vol.122 , pp. 145-157
    • Chen, W.1    Li, C.2
  • 8
    • 0002166459 scopus 로고
    • Chemotactic collapse in two dimensions
    • Childress, S., 1984. Chemotactic collapse in two dimensions. Lecture Notes in Biomath, 55: 61-66.
    • (1984) Lecture Notes in Biomath , vol.55 , pp. 61-66
    • Childress, S.1
  • 9
    • 0019784884 scopus 로고
    • Nonlinear aspects of chemotaxis
    • Childress, S., and Percus, J. K., 1981. Nonlinear aspects of chemotaxis. Math. Bioscience, 56: 217-237.
    • (1981) Math. Bioscience , vol.56 , pp. 217-237
    • Childress, S.1    Percus, J.K.2
  • 11
    • 34250271532 scopus 로고
    • Symmetry and related properties via the maximum principle
    • Gidas, B., Ni, W. M., and Nirenberg, L., 1979. Symmetry and related properties via the maximum principle. Comm. Math. Phys, 68: 209-243.
    • (1979) Comm. Math. Phys , vol.68 , pp. 209-243
    • Gidas, B.1    Ni, W.M.2    Nirenberg, L.3
  • 13
    • 84966208077 scopus 로고
    • On explosion of solutions to a system of partial differential equations modeling chemotaxis
    • Jager, W., and Luckhaus, S., 1992. On explosion of solutions to a system of partial differential equations modeling chemotaxis. Trans. Amer. Math. Soc, 392: 819-824.
    • (1992) Trans. Amer. Math. Soc , vol.392 , pp. 819-824
    • Jager, W.1    Luckhaus, S.2
  • 14
    • 0002010985 scopus 로고
    • Curvature functions for compact 2 manifolds
    • Kazdan, J. L., and Warner, F. W., 1967. Curvature functions for compact 2 manifolds. Ann. Math, 99: 14-47.
    • (1967) Ann. Math , vol.99 , pp. 14-47
    • Kazdan, J.L.1    Warner, F.W.2
  • 15
    • 0015010990 scopus 로고
    • Traveling bands of Chemotactic Bacteria: A theoretical analysis
    • Keller, E. F., and Segel, L. A., 1971. Traveling bands of Chemotactic Bacteria: A theoretical analysis. J. Theor. Biol, 30: 235-248.
    • (1971) J. Theor. Biol , vol.30 , pp. 235-248
    • Keller, E.F.1    Segel, L.A.2
  • 16
    • 0001759122 scopus 로고
    • Blow up analysis for solutions of in dimension two
    • Li, Y. Y., and Shafir, I., 1994. Blow up analysis for solutions of in dimension two. Ind. Univ. Math. J, 43: 1255-1270.
    • (1994) Ind. Univ. Math. J , vol.43 , pp. 1255-1270
    • Li, Y.Y.1    Shafir, I.2
  • 18
    • 0000911252 scopus 로고
    • Blow up of radially symmetric solutions to a chemotaxis system
    • Nagai, T., 1995. Blow up of radially symmetric solutions to a chemotaxis system. Advances in Math. Science and Appl, 5: 581-601.
    • (1995) Advances in Math. Science and Appl , vol.5 , pp. 581-601
    • Nagai, T.1
  • 19
    • 0015757937 scopus 로고
    • Chemotaxis, signal relaying and aggregation morphology
    • Nanjundiah, V., 1973. Chemotaxis, signal relaying and aggregation morphology. J. Theor. Biol, 42: 63-105.
    • (1973) J. Theor. Biol , vol.42 , pp. 63-105
    • Nanjundiah, V.1
  • 20
    • 0001247391 scopus 로고
    • Large time behavior of the heat kernel and the behavior of the Green function near criticality for nonsymmetric elliptic operators
    • Pinchover, Y., 1991. Large time behavior of the heat kernel and the behavior of the Green function near criticality for nonsymmetric elliptic operators. J. Func. Anal, 104: 54-70.
    • (1991) J. Func. Anal , vol.104 , pp. 54-70
    • Pinchover, Y.1
  • 21
    • 21144461798 scopus 로고
    • On steady distributions of self attracting clusters under friction and fluctuations
    • Wolansky, G., 1992. On steady distributions of self attracting clusters under friction and fluctuations. Arch. Rational Mech. Anal, 119: 355-391.
    • (1992) Arch. Rational Mech. Anal , vol.119 , pp. 355-391
    • Wolansky, G.1
  • 22
    • 51249166872 scopus 로고
    • On the evolution of self interacting clusters and applications to semi linear equations with exponential nonlinearity
    • Wolansky, G., 1992. On the evolution of self interacting clusters and applications to semi linear equations with exponential nonlinearity. J. d'Analyse Math, 59: 251-272.
    • (1992) J. d'Analyse Math , vol.59 , pp. 251-272
    • Wolansky, G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.