Time-space white noise eliminates global solutions in reaction-diffusion equations
We prove that perturbing the reaction-diffusion equation ut = ux x + (u+)p (p > 1), with time-space white noise produces that solutions explodes with probability one for every initial datum, opposite to the deterministic model where a positive stationary solution exists. © 2008 Elsevier B.V....
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2009
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| 008 | 190411s2009 xx ||||fo|||| 00| 0 eng|d | ||
| 024 | 7 | |2 scopus |a 2-s2.0-58149175805 | |
| 040 | |a Scopus |b spa |c AR-BaUEN |d AR-BaUEN | ||
| 030 | |a PDNPD | ||
| 100 | 1 | |a Fernández Bonder, J. | |
| 245 | 1 | 0 | |a Time-space white noise eliminates global solutions in reaction-diffusion equations |
| 260 | |c 2009 | ||
| 270 | 1 | 0 | |m Fernández Bonder, J.; Departamento de Matemática, FCEyN, Universidad de Buenos Aires, Pabellon I, Ciudad Universitaria, 1428 Buenos Aires, Argentina; email: jfbonder@dm.uba.ar |
| 506 | |2 openaire |e Política editorial | ||
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| 504 | |a Budd, C.J., Huang, W., Russell, R.D., Moving mesh methods for problems with blow-up (1996) SIAM J. Sci. Comput., 17 (2), pp. 305-327 | ||
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| 504 | |a Galaktionov, V.A., Vázquez, J.L., The problem of blow-up in nonlinear parabolic equations (2002) Discrete Contin. Dyn. Syst., 8 (2), pp. 399-433. , Current developments in partial differential equations (Temuco, 1999) | ||
| 504 | |a Ferreira, R., Groisman, P., Rossi, J.D., Numerical blow-up for the porous medium equation with a source (2004) Numer. Methods Partial Differential Equations, 20 (4), pp. 552-575 | ||
| 504 | |a Ferreira, R., Groisman, P., Rossi, J.D., Adaptive numerical schemes for a parabolic problem with blow-up (2003) IMA J. Numer. Anal., 23 (3), pp. 439-463 | ||
| 504 | |a Groisman, P., Totally discrete explicit and semi-implicit Euler methods for a blow-up problem in several space dimensions (2006) Computing, 76 (3-4), pp. 325-352 | ||
| 504 | |a Gyöngy, I., Lattice approximations for stochastic quasi-linear parabolic partial differential equations driven by space-time white noise I (1998) Potential Anal., 9, pp. 1-25 | ||
| 504 | |a Gyöngy, I., Pardoux, É., On the regularization effect of space-time white noise on quasi-linear parabolic partial differential equations (1993) Probab. Theory Related Fields, 97 (1-2), pp. 211-229 | ||
| 504 | |a Karatzas, I., Shreve, S.E., (1991) Graduate Texts in Mathematics, 113. , Springer-Verlag, New York | ||
| 504 | |a Mao, X., Marion, G., Renshaw, E., Environmental Brownian noise suppresses explosions in population dynamics (2002) Stochastic Process. Appl., 97 (1), pp. 95-110 | ||
| 504 | |a Mueller, C., Long-time existence for signed solutions of the heat equation with a noise term (1998) Probab. Theory Related Fields, 110 (1), pp. 51-68 | ||
| 504 | |a Mueller, C., The critical parameter for the heat equation with a noise term to blow up in finite time (2000) Ann. Probab., 28 (4), pp. 1735-1746 | ||
| 504 | |a Mueller, C., Sowers, R., Blowup for the heat equation with a noise term (1993) Probab. Theory Related Fields, 97 (3), pp. 287-320 | ||
| 504 | |a É Pardoux, Spdes Mini Course Given at Fudan University, Shanghai, April 2007. http://www.cmi.univ-mrs.fr/~pardoux/spde-fudan.pdf; Samarskii, A.A., Galaktionov, V.A., Kurdyumov, S.P., Mikhailov, A.P., Blow-up in quasilinear parabolic equations (1995) de Gruyter Expositions in Mathematics, 19. , Walter de Gruyter & Co., Berlin Translated from the 1987 Russian original by Michael Grinfeld and revised by the authors | ||
| 504 | |a Walsh, J.B., An introduction to stochastic partial differential equations (1986) Lecture Notes in Math., 1180, pp. 265-439. , École d'été de probabilités de Saint-Flour, XIV-1984, Springer, Berlin | ||
| 520 | 3 | |a We prove that perturbing the reaction-diffusion equation ut = ux x + (u+)p (p > 1), with time-space white noise produces that solutions explodes with probability one for every initial datum, opposite to the deterministic model where a positive stationary solution exists. © 2008 Elsevier B.V. All rights reserved. |l eng | |
| 593 | |a Departamento de Matemática, FCEyN, Universidad de Buenos Aires, Pabellon I, Ciudad Universitaria, 1428 Buenos Aires, Argentina | ||
| 690 | 1 | 0 | |a EXPLOSION |
| 690 | 1 | 0 | |a REACTION-DIFFUSION EQUATIONS |
| 690 | 1 | 0 | |a STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS |
| 690 | 1 | 0 | |a COMPUTATIONAL FLUID DYNAMICS |
| 690 | 1 | 0 | |a DIFFUSION |
| 690 | 1 | 0 | |a DIFFUSION IN LIQUIDS |
| 690 | 1 | 0 | |a IMAGE SEGMENTATION |
| 690 | 1 | 0 | |a WHITE NOISE |
| 690 | 1 | 0 | |a DETERMINISTIC MODELS |
| 690 | 1 | 0 | |a GLOBAL SOLUTIONS |
| 690 | 1 | 0 | |a NOISE ELIMINATES |
| 690 | 1 | 0 | |a REACTION-DIFFUSION EQUATIONS |
| 690 | 1 | 0 | |a STATIONARY SOLUTIONS |
| 690 | 1 | 0 | |a STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS |
| 690 | 1 | 0 | |a PARTIAL DIFFERENTIAL EQUATIONS |
| 700 | 1 | |a Groisman, P. | |
| 773 | 0 | |d 2009 |g v. 238 |h pp. 209-215 |k n. 2 |p Phys D Nonlinear Phenom |x 01672789 |w (AR-BaUEN)CENRE-277 |t Physica D: Nonlinear Phenomena | |
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| 856 | 4 | 0 | |u https://doi.org/10.1016/j.physd.2008.09.005 |y DOI |
| 856 | 4 | 0 | |u https://hdl.handle.net/20.500.12110/paper_01672789_v238_n2_p209_FernandezBonder |y Handle |
| 856 | 4 | 0 | |u https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01672789_v238_n2_p209_FernandezBonder |y Registro en la Biblioteca Digital |
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| 999 | |c 69939 | ||