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Volumn 61, Issue 2, 2003, Pages 101-134

Perturbative methods in scales of Banach spaces: Applications for Gevrey regularity of solutions to semilinear partial differential equations

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EID: 18544375593     PISSN: 03731243     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Conference Paper
Times cited : (9)

References (55)
  • 1
    • 0033331683 scopus 로고    scopus 로고
    • Solitary waves solution of the Benjamin equation
    • ALBERT J., BONA J.L. AND RESTREPO J.M., Solitary waves solution of the Benjamin equation, SIAM J. Appl. Math. 59 6 (1999), 2139-2161.
    • (1999) SIAM J. Appl. Math. , vol.59 , Issue.6 , pp. 2139-2161
    • Albert, J.1    Bona, J.L.2    Restrepo, J.M.3
  • 2
    • 0033540592 scopus 로고    scopus 로고
    • Existence and stability of solitary wave solutions of the Benjamin equation
    • ANGULO J., Existence and stability of solitary wave solutions of the Benjamin equation, J. Diff. Eq. 152 (1999), 136-159.
    • (1999) J. Diff. Eq. , vol.152 , pp. 136-159
    • Angulo, J.1
  • 3
    • 0000823596 scopus 로고    scopus 로고
    • The initial value problem for the generalized Burgers' equation
    • BEKHIRANOV D., The initial value problem for the generalized Burgers' equation, Diff. Int. Eq. 9 (1996), 1253-1265.
    • (1996) Diff. Int. Eq. , vol.9 , pp. 1253-1265
    • Bekhiranov, D.1
  • 5
    • 0043265783 scopus 로고    scopus 로고
    • Parabolic equations with conservative nonlinear term and singular initial data
    • Proceedings of the Second World Congress of Nonlinear Analysts, Part 4 (Athens, 1996)
    • BIAGIONI H.A., CADEDDU L. AND GRAMCHEV T., Parabolic equations with conservative nonlinear term and singular initial data, Proceedings of the Second World Congress of Nonlinear Analysts, Part 4 (Athens, 1996), Nonlinear Anal. 30 4 (1997), 2489-2496.
    • (1997) Nonlinear Anal. , vol.30 , Issue.4 , pp. 2489-2496
    • Biagioni, H.A.1    Cadeddu, L.2    Gramchev, T.3
  • 6
    • 0032110796 scopus 로고    scopus 로고
    • Evolution PDE with elliptic dissipative terms: Critical index for singular initial data, self-similar solutions and analytic regularity
    • BIAGIONI H.A. AND GRAMCHEV T., Evolution PDE with elliptic dissipative terms: critical index for singular initial data, self-similar solutions and analytic regularity, C. R. Acad. Sci. Paris Sér. I Math. 327 1 (1998), 41-46.
    • (1998) C. R. Acad. Sci. Paris Sér. I Math. , vol.327 , Issue.1 , pp. 41-46
    • Biagioni, H.A.1    Gramchev, T.2
  • 7
    • 0004434530 scopus 로고    scopus 로고
    • Multidimensional Kuramoto-Sivashinsky type equations: Singular initial data and analytic regularity
    • Proceedings of the Fifth Workshop on Partial Differential Equations, (Rio de Janeiro, 1997)
    • BIAGIONI H.A. AND GRAMCHEV T., Multidimensional Kuramoto-Sivashinsky type equations: singular initial data and analytic regularity, Proceedings of the Fifth Workshop on Partial Differential Equations, (Rio de Janeiro, 1997), Matematica Contemporanea 15 (1998), 21-42.
    • (1998) Matematica Contemporanea , vol.15 , pp. 21-42
    • Biagioni, H.A.1    Gramchev, T.2
  • 10
    • 0002112502 scopus 로고    scopus 로고
    • Existence and asymptotic properties of solitary-wave solutions of Benjamin-type equations
    • BONA J. AND CHEN H., Existence and asymptotic properties of solitary-wave solutions of Benjamin-type equations, Adv. Diff. Eq. 3 (1998), 51-84.
    • (1998) Adv. Diff. Eq. , vol.3 , pp. 51-84
    • Bona, J.1    Chen, H.2
  • 11
    • 0031142252 scopus 로고    scopus 로고
    • Decay and analyticity of solitary waves
    • BONA J. AND LI Y., Decay and analyticity of solitary waves, J. Math. Pures Appl. 76 (1997), 377-430.
    • (1997) J. Math. Pures Appl. , vol.76 , pp. 377-430
    • Bona, J.1    Li, Y.2
  • 13
    • 0000234264 scopus 로고
    • Pseudo-differential operators and Gevrey classes
    • BOUTET DE MONVEL L. AND KRÉE P., Pseudo-differential operators and Gevrey classes, Ann. Inst. Fourier 17 1 (1967), 295-323.
    • (1967) Ann. Inst. Fourier , vol.17 , Issue.1 , pp. 295-323
    • Boutet De Monvel, L.1    Krée, P.2
  • 14
    • 0002538991 scopus 로고
    • Nonlinear parabolic equations involving measures as initial conditions
    • BREZIS H. AND FRIEDMAN A., Nonlinear parabolic equations involving measures as initial conditions, J. Math. Pures Appl. 62 (1983), 73-97.
    • (1983) J. Math. Pures Appl. , vol.62 , pp. 73-97
    • Brezis, H.1    Friedman, A.2
  • 15
    • 0030443821 scopus 로고    scopus 로고
    • A nonlinear heat equation with singular initial data
    • BREZIS H. AND CAZENAVE T., A nonlinear heat equation with singular initial data, J. Anal. Math. 68 (1996), 277-304.
    • (1996) J. Anal. Math. , vol.68 , pp. 277-304
    • Brezis, H.1    Cazenave, T.2
  • 17
    • 18544377559 scopus 로고    scopus 로고
    • Pseudodifferential parametrices of infinite order for SG-hyperbolic problems
    • to appear
    • CAPPIELLO M., Pseudodifferential parametrices of infinite order for SG-hyperbolic problems, Rend. Sem. Univ. e Polit. Torino, to appear.
    • Rend. Sem. Univ. e Polit. Torino
    • Cappiello, M.1
  • 19
    • 0001923237 scopus 로고
    • Au delà des opérateurs pseudo-différentiels
    • Société Mathématique de France, Paris
    • COIFFMAN R. AND MEYER Y., Au delà des opérateurs pseudo-différentiels, Astérisque 57, Société Mathématique de France, Paris 1978.
    • (1978) Astérisque , vol.57
    • Coiffman, R.1    Meyer, Y.2
  • 20
    • 0042745515 scopus 로고    scopus 로고
    • Local solvability and hypoellipticity for semi-linear anisotropic partial differential equations
    • DEDONNO G. AND OLIARO A., Local solvability and hypoellipticity for semi-linear anisotropic partial differential equations, Trans. Amer. Math. Soc. 355 (2003), 3405-3432
    • (2003) Trans. Amer. Math. Soc. , vol.355 , pp. 3405-3432
    • Dedonno, G.1    Oliaro, A.2
  • 21
    • 0030537418 scopus 로고    scopus 로고
    • Nonuniqueness and uniqueness in the initial-value problem for Burgers' equation
    • Dix D., Nonuniqueness and uniqueness in the initial-value problem for Burgers' equation, SIAM J. Math. Anal. 27 3 (1996), 708-724.
    • (1996) SIAM J. Math. Anal. , vol.27 , Issue.3 , pp. 708-724
    • Dix, D.1
  • 22
    • 0002062139 scopus 로고    scopus 로고
    • Gevrey regularity for nonlinear analytic parabolic equations
    • FERRARI A. AND TITI E., Gevrey regularity for nonlinear analytic parabolic equations, Comm. Partial Diff. Eq. 23 (1998), 1-16.
    • (1998) Comm. Partial Diff. Eq. , vol.23 , pp. 1-16
    • Ferrari, A.1    Titi, E.2
  • 23
    • 33746636159 scopus 로고
    • Gevrey class regularity for the solutions of the Navier-Stokes equations
    • FOIAS C. AND TEMAM R., Gevrey class regularity for the solutions of the Navier-Stokes equations, J. Funct. Anal. 87 (1989), 359-369.
    • (1989) J. Funct. Anal. , vol.87 , pp. 359-369
    • Foias, C.1    Temam, R.2
  • 25
    • 0000924617 scopus 로고
    • n
    • Mathematical Analysis and applications, Part A, Academic Press, New York, London
    • n, Mathematical Analysis and applications, Part A, Adv. in Math. Suppl. Stud. 7a, Academic Press, New York, London 1981, 369-402.
    • (1981) Adv. in Math. Suppl. Stud. , vol.7 A , pp. 369-402
    • Gidas, B.1    Ni, W.M.2    Nirenberg, L.3
  • 26
    • 0000972882 scopus 로고    scopus 로고
    • Problème de Goursat non linéaire dans les espaces de Gevrey pour les équations de Kirchhoff généralisées
    • GOURDIN D. AND MECHAB M., Problème de Goursat non linéaire dans les espaces de Gevrey pour les équations de Kirchhoff généralisées, J. Math. Pures Appl. 75 6 (1996), 569-593.
    • (1996) J. Math. Pures Appl. , vol.75 , Issue.6 , pp. 569-593
    • Gourdin, D.1    Mechab, M.2
  • 27
    • 0001970196 scopus 로고    scopus 로고
    • Solvability in Gevrey classes for semilinear PDE with multiple characteristics
    • GRAMCHEV T. AND RODINO L., Solvability in Gevrey classes for semilinear PDE with multiple characteristics, Boll. Un. Mat. Ital. 2-B 8 (1999), 65-120.
    • (1999) Boll. Un. Mat. Ital. , vol.2 B , Issue.8 , pp. 65-120
    • Gramchev, T.1    Rodino, L.2
  • 28
    • 0033408735 scopus 로고    scopus 로고
    • Rapidly convergent iteration method for simultaneous normal forms of commuting maps
    • GRAMCHEV T. AND YOSHINO M., Rapidly convergent iteration method for simultaneous normal forms of commuting maps, Math. Z. 231 (1999), 745-770.
    • (1999) Math. Z. , vol.231 , pp. 745-770
    • Gramchev, T.1    Yoshino, M.2
  • 29
    • 0039399924 scopus 로고    scopus 로고
    • Solitary wave solutions to a class of fifth-order model equations
    • GROVES M.D., Solitary wave solutions to a class of fifth-order model equations, Nonlinearity 11 (1998), 341-353.
    • (1998) Nonlinearity , vol.11 , pp. 341-353
    • Groves, M.D.1
  • 31
    • 22644449518 scopus 로고    scopus 로고
    • Travelling-waves for the FKPP equation via probabilistic arguments
    • HARRIS S., Travelling-waves for the FKPP equation via probabilistic arguments, Proc. Roy. Soc. Edinburgh (A) 129 3 (1999), 503-517.
    • (1999) Proc. Roy. Soc. Edinburgh (A) , vol.129 , Issue.3 , pp. 503-517
    • Harris, S.1
  • 32
    • 0003304963 scopus 로고
    • Geometric theory of semilinear parabolic equations
    • Springer, Berlin
    • HENRY D., Geometric theory of semilinear parabolic equations, Lecture Notes in Mathematics 840, Springer, Berlin 1981.
    • (1981) Lecture Notes in Mathematics , vol.840
    • Henry, D.1
  • 34
    • 0141859724 scopus 로고
    • Spectral methods in soliton equations
    • Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, New York
    • ILIEV I.D., KHRISTOV E.KH. AND K.P. KIRCHEV, Spectral methods in soliton equations, Pitman Monographs and Surveys in Pure and Applied Mathematics 73, Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, New York 1994
    • (1994) Pitman Monographs and Surveys in Pure and Applied Mathematics , vol.73
    • Iliev, I.D.1    Khristov, E.Kh.2    Kirchev, K.P.3
  • 35
    • 0002261849 scopus 로고
    • Local solution of Cauchy problem for nonlinear hyperbolic systems in Gevrey classes
    • KAJITANI K., Local solution of Cauchy problem for nonlinear hyperbolic systems in Gevrey classes, Hokkaido Math. J. 12 3 (1983), 434-460.
    • (1983) Hokkaido Math. J. , vol.12 , Issue.3 , pp. 434-460
    • Kajitani, K.1
  • 36
    • 51649139542 scopus 로고
    • s-solutions and unconditional well-posedness
    • s-solutions and unconditional well-posedness, J. Anal. Math., 67 (1995), 281-306.
    • (1995) J. Anal. Math. , vol.67 , pp. 281-306
    • Kato, T.1
  • 37
    • 0034691324 scopus 로고    scopus 로고
    • Uniqueness of the stationary wave for the extended Fisher-Kolmogorov equation
    • KWAPISZ J., Uniqueness of the stationary wave for the extended Fisher-Kolmogorov equation, J. Diff. Eq. 165 1 (2000), 235-253.
    • (2000) J. Diff. Eq. , vol.165 , Issue.1 , pp. 235-253
    • Kwapisz, J.1
  • 38
    • 0000946209 scopus 로고
    • Semilinear heat equations and the Navier-Stokes equation with distributions in new function spaces as initial data
    • KOZONO H. AND YAMAZAKI M., Semilinear heat equations and the Navier-Stokes equation with distributions in new function spaces as initial data, Comm. Partial Diff. Eq. 19 (1994), 959-1014.
    • (1994) Comm. Partial Diff. Eq. , vol.19 , pp. 959-1014
    • Kozono, H.1    Yamazaki, M.2
  • 39
    • 0000873295 scopus 로고    scopus 로고
    • Distribution-valued initial data for the complex Ginzburg-Landau equation
    • LEVERMORE D. AND OLIVER M., Distribution-valued initial data for the complex Ginzburg-Landau equation, Comm. Partial Differential Equations 22 (1997), 39-49.
    • (1997) Comm. Partial Differential Equations , vol.22 , pp. 39-49
    • Levermore, D.1    Oliver, M.2
  • 40
    • 0030545823 scopus 로고    scopus 로고
    • Analyticity of solitary-wave solutions of model equations for long waves
    • Li Y. AND BONA J., Analyticity of solitary-wave solutions of model equations for long waves, SIAM J. Math. Anal. 27 3 (1997) 725-737.
    • (1997) SIAM J. Math. Anal. , vol.27 , Issue.3 , pp. 725-737
    • Li, Y.1    Bona, J.2
  • 41
    • 25544449558 scopus 로고
    • Steady solutions of the Kuramoto-Sivashinsky equation
    • MICHELSON D., Steady solutions of the Kuramoto-Sivashinsky equation, Phys. D 19 1 (1986), 89-111.
    • (1986) Phys. D , vol.19 , Issue.1 , pp. 89-111
    • Michelson, D.1
  • 42
    • 0003297871 scopus 로고
    • Nonlinear nonlocal equations in the theory of waves
    • American Mathematical Society, Providence, RI
    • NAUMKIN P. AND SHISHMAREV I., Nonlinear nonlocal equations in the theory of waves, Transl. of Math. Monographs 133, American Mathematical Society, Providence, RI 1994.
    • (1994) Transl. of Math. Monographs , vol.133
    • Naumkin, P.1    Shishmarev, I.2
  • 43
    • 0003292314 scopus 로고
    • Multiplication of distributions and applications to partial differential equations
    • Longman Scientifi & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York
    • OBERGUGGENBERGER M., Multiplication of distributions and applications to partial differential equations, Pitman Research Notes in Mathematics Series 259, Longman Scientifi & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York 1992.
    • (1992) Pitman Research Notes in Mathematics Series , vol.259
    • Oberguggenberger, M.1
  • 45
    • 0034347241 scopus 로고    scopus 로고
    • Invariant tori, effective stability, and quasimodes with exponentially small error terms, I. Birkoff normal forms
    • POPOV G., Invariant tori, effective stability, and quasimodes with exponentially small error terms, I. Birkoff normal forms, Ann. Henri Poincaré 1 (2000), 223-248.
    • (2000) Ann. Henri Poincaré , vol.1 , pp. 223-248
    • Popov, G.1
  • 47
    • 18544372518 scopus 로고    scopus 로고
    • preprint(2003)
    • RABIER P.J.,preprint(2003).
    • Rabier, P.J.1
  • 48
    • 0034691323 scopus 로고    scopus 로고
    • Exponential decay of the solutions of quasilinear second order equations and Pohozaev identities
    • RABIER P.J. AND STUART C., Exponential decay of the solutions of quasilinear second order equations and Pohozaev identities, J. Diff. Eq. 165 (2000), 199-234.
    • (2000) J. Diff. Eq. , vol.165 , pp. 199-234
    • Rabier, P.J.1    Stuart, C.2
  • 49
    • 0031492827 scopus 로고    scopus 로고
    • Semilinear parabolic equations with distributions as initial data
    • RIBAUD F., Semilinear parabolic equations with distributions as initial data, Discrete Contin. Dynam. Systems 3 (1997), 305-316.
    • (1997) Discrete Contin. Dynam. Systems , vol.3 , pp. 305-316
    • Ribaud, F.1
  • 51
    • 0022130031 scopus 로고
    • Application of pole decomposition to an equation governing the dynamics of wrinkled flame fronts
    • THUAL O., FRISCH U. AND HÉNON M., Application of pole decomposition to an equation governing the dynamics of wrinkled flame fronts, J. Physique 46 (1985), 1485-1494.
    • (1985) J. Physique , vol.46 , pp. 1485-1494
    • Thual, O.1    Frisch, U.2    Hénon, M.3
  • 53
    • 0030530210 scopus 로고    scopus 로고
    • Analyticity for essentially bounded solutions to strongly parabolic semilinear systems
    • TAKÀČ P., BOLLERMAN P., DOELMAN A., VAN HARTEN A. AND TITI E.,Analyticity for essentially bounded solutions to strongly parabolic semilinear systems, SIAM J. Math. Anal. 27 (1996), 424-448.
    • (1996) SIAM J. Math. Anal. , vol.27 , pp. 424-448
    • Takàč, P.1    Bollerman, P.2    Doelman, A.3    Van Harten, A.4    Titi, E.5
  • 55
    • 0034206088 scopus 로고    scopus 로고
    • Front propagation in heterogeneous media
    • XIN J., Front propagation in heterogeneous media, SIAM Review 42 2 (2000), 161-230.
    • (2000) SIAM Review , vol.42 , Issue.2 , pp. 161-230
    • Xin, J.1


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