| dc.creator | Biagioni H.A. | |
| dc.creator | Gramchev T. | |
| dc.date | 2003 | |
| dc.date | 2015-06-30T17:33:09Z | |
| dc.date | 2015-11-26T14:12:43Z | |
| dc.date | 2015-06-30T17:33:09Z | |
| dc.date | 2015-11-26T14:12:43Z | |
| dc.date.accessioned | 2018-03-28T21:13:24Z | |
| dc.date.available | 2018-03-28T21:13:24Z | |
| dc.identifier | | |
| dc.identifier | Journal Of Differential Equations. , v. 194, n. 1, p. 140 - 165, 2003. | |
| dc.identifier | 220396 | |
| dc.identifier | 10.1016/S0022-0396(03)00197-9 | |
| dc.identifier | http://www.scopus.com/inward/record.url?eid=2-s2.0-0141656254&partnerID=40&md5=41612431d543de9a13a6636d7659cbdb | |
| dc.identifier | http://www.repositorio.unicamp.br/handle/REPOSIP/102623 | |
| dc.identifier | http://repositorio.unicamp.br/jspui/handle/REPOSIP/102623 | |
| dc.identifier | 2-s2.0-0141656254 | |
| dc.identifier.uri | http://repositorioslatinoamericanos.uchile.cl/handle/2250/1242082 | |
| dc.description | We propose a unified functional analytic approach to study the uniform analytic-Gevrey regularity and the decay of solutions to semilinear elliptic equations on ℝn. First, we develop a fractional calculus for nonlinear maps in Banach spaces of Lp based Gevrey functions, 1 < p < ∞. Then we propose an abstract result on uniform analytic Gevrey regularity, which covers as particular cases solitary wave solutions to both dispersive and dissipative equations. We require a priori low Hp s(ℝn) regularity, with s > scr > 0 depending on the nonlinearity. Next, we investigate the type of decay - polynomial or exponential - of the derivatives of solutions to semilinear elliptic equations, provided they decay a priori slowly as o( x -τ), x → ∞ for some small τ > 0. The restrictions, involved in our results, are optimal. In particular, given a hyperplane L, we construct 2d - 2 strongly singular solutions (locally in Hp s(ℝn) for s < scr) to the semilinear Laplace equation Δu + cud = 0, whose singularities are concentrated on L. © 2003 Elsevier Inc. All rights reserved. | |
| dc.description | 194 | |
| dc.description | 1 | |
| dc.description | 140 | |
| dc.description | 165 | |
| dc.description | Albert, J., Bona, J., Restrepo, J., Solitary waves solution of the Benjamin equation (1999) SIAM J. Appl. Math., 59, pp. 2139-2161 | |
| dc.description | Angulo, J., Existence and stability of solitary wave solutions of the Benjamin equation (1999) J. Differential Equations, 152, pp. 136-159 | |
| dc.description | Benjamin, T.B., Bona, J.L., Mahony, J.J., Model equations for long waves in nonlinear dispersive systems (1972) Philos. Trans. Roy. Soc. London Ser. A, 272, pp. 47-78 | |
| dc.description | Biagioni, H.A., Cadeddu, L., Gramchev, T., Semilinear parabolic equations with singular data in anisotropic weighted spaces (1999) Differential Integral Equations, 12 (5), pp. 613-636 | |
| dc.description | Biagioni, H.A., Gramchev, T., Evolution PDE with elliptic dissipative terms: Critical index for singular initial data, self-similar solutions and analytic regularity (1998) C.R. Acad. Sci. Paris Sér. I, 327, pp. 41-46 | |
| dc.description | Biler, P., Woyczyński, W., Nonlocal quadratic evolution problems (2000) Evolution Equations: Existence, Regularity and Singularities, 52, pp. 11-24. , (Warsaw, 1998) Banach Center Publ., (Warsaw, 1998), Polish Acad. Sci., Warsaw | |
| dc.description | Bona, J., Chen, H., Existence and asymptotic properties of solitary-wave solutions of Benjamin-type equations (1998) Adv. Differential Equations, 3, pp. 51-84 | |
| dc.description | Bona, J., Li, Y., Decay and analyticity of solitary waves (1997) J. Math. Pures Appl., 76, pp. 377-430 | |
| dc.description | Bourdaud, G., Reissig, M., Sickel, W., Hyperbolic equations, function spaces with exponential weights and Nemytskij operators (2001), preprintBoutet de Monvel, L., Krée, P., Pseudo-differential operators and Gevrey classes (1967) Ann. Inst. Fourier, 17, pp. 295-323. , (fasc. 1) | |
| dc.description | Brezis, H., Cazenave, T., A nonlinear heat equation with singular initial data (1996) J. Anal. Math., 68, pp. 277-304 | |
| dc.description | Coiffman, R., Meyer, Y., Au delà des opérateurs pseudo-différentiels (1978) Astérisque, 57. , Société Mathématique de France, Paris | |
| dc.description | Dix, D., Nonuniqueness and uniqueness in the initial-value problem for Burgers' equation (1996) SIAM J. Math. Anal., 27 (3), pp. 708-724 | |
| dc.description | Foias, C., Temam, R., Gevrey class regularity for the solutions of the Navier-Stokes equations (1989) J. Funct. Anal., 87, pp. 359-369 | |
| dc.description | Gidas, B., Ni, W.M., Nirenberg, L., Symmetry of positive solutions of nonlinear elliptic equations in ℝn (1981) Mathematical Analysis and Applications Part A, Advances in Mathematical Supplementary Studies, 7 A, pp. 369-402. , Academic Press, New York, London | |
| dc.description | Gourdin, D., Mechab, M., Problème de Goursat non linéaire dans les espaces de Gevrey pour les équations de Kirchhoff généralisées (1996) J. Math. Pures Appl., 75 (6), pp. 569-593. , (9) | |
| dc.description | Gramchev, T., Rodino, L., Solvability in Gevrey classes for semilinear PDE with multiple characteristics (1999) Boll. Un. Mat. Ital., 2 B (8), pp. 65-120 | |
| dc.description | Gramchev, T., Yoshino, M., Rapidly convergent iteration method for simultaneous normal forms of commuting maps (1999) Math. Z., 231, pp. 745-770 | |
| dc.description | Groves, M.D., Solitary wave solutions to a class of fifth-order model equations (1998) Nonlinearity, 11, pp. 341-353 | |
| dc.description | Grujić, Z., Kukavica, I., Space analyticity for the Navier-Stokes and related equations with initial data in Lp (1998) J. Funct. Anal., 152 (2), pp. 447-466 | |
| dc.description | Harris, S., Travelling-waves for the FKPP equation via probabilistic arguments (1999) Proc. Roy. Soc. Edinburgh Sect. A, 129 (3), pp. 503-517 | |
| dc.description | Henry, D., Geometric Theory of Semilinear Parabolic Equations (1981) Lecture Notes in Mathematics, 840. , Springer, Berlin | |
| dc.description | Hörmander, L., (1983) The Analysis of Linear Partial Differential Operators, 1-4. , Springer, Berlin | |
| dc.description | Iliev, I.D., Khristov, E.Kh., Kirchev, K.P., Spectral Methods in Soliton Equations (1994) Pitman Monographs and Surveys in Pure and Applied Mathematics, 73. , Longman Scientific & Technical, Harlow | |
| dc.description | copublished in the United States with Wiley, Inc., New York | |
| dc.description | Kato, T., On nonlinear Schrödinger equations, II. Hs-solutions and unconditional well-posedness (1995) J. Anal. Math., 67, pp. 281-306 | |
| dc.description | Kwapisz, J., Uniqueness of the stationary wave for the extended Fisher-Kolmogorov equation (2000) J. Differential Equations, 165 (1), pp. 235-253 | |
| dc.description | Li, Y., Bona, J., Analyticity of solitary-wave solutions of model equations for long waves (1997) SIAM J. Math. Anal., 27 (3), pp. 725-737 | |
| dc.description | Michelson, D., Steady solutions of the Kuramoto-Sivashinsky equation (1986) Physics D, 19, pp. 89-111 | |
| dc.description | Naumkin, P., Shishmarev, I., Nonlinear Nonlocal Equations in the Theory of Waves (1994) Translations of Mathematical Monographs, 133. , American Mathematical Society, Providence, RI | |
| dc.description | Oberguggenberger, M., Multiplication of Distributions and Applications to Partial Differential Equations (1992) Pitman Research Notes in Mathematics Series, 259. , Longman Scientific & Technical, Harlow | |
| dc.description | copublished in the United States with Wiley, Inc., New York | |
| dc.description | Oliver, M., Titi, E., Remark on the rate of decay of higher order derivatives for solutions to the Navier-Stokes equations in ℝn (2000) J. Funct. Anal., 172, pp. 1-18 | |
| dc.description | Rabier, P.J., Stuart, C., Exponential decay of the solutions of quasilinear second-order equations and Pohozaev identities (2000) J. Differential Equations, 165, pp. 199-234 | |
| dc.description | Ribaud, F., Semilinear parabolic equations with distributions as initial data (1997) Discrete Continuous Dyn. Systems, 3, pp. 305-316 | |
| dc.description | Rodino, L., Linear Partial Differential Operators in Gevrey Spaces (1993), World Scientific Publishing Co., Inc., River Edge, NJ, x + 251 ppShubin, M., Pseudodifferential Operators and the Spectral Theory (1987), Springer Series in Soviet Mathematics, Springer, BerlinThual, O., Frisch, U., Hénon, M., Application of pole decomposition to an equation governing the dynamics of wrinkled flame fronts (1985) J. Physique, 46, pp. 1485-1494 | |
| dc.description | Triebel, H., Theory of Function Spaces (1988), Birkhäuser, BaselXin, J., Front propagation in heterogeneous media (2000) SIAM Rev., 42 (2), pp. 161-230 | |
| dc.language | en | |
| dc.publisher | | |
| dc.relation | Journal of Differential Equations | |
| dc.rights | fechado | |
| dc.source | Scopus | |
| dc.title | Fractional Derivative Estimates In Gevrey Spaces, Global Regularity And Decay For Solutions To Semilinear Equations In ℝn | |
| dc.type | Artículos de revistas | |
