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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Autor principal: Fernández Bonder, J.
Otros Autores: Groisman, P.
Formato: Capítulo de libro
Lenguaje:Inglés
Publicado: 2009
Acceso en línea:Registro en Scopus
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Registro en la Biblioteca Digital
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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 Buckdahn, R., Pardoux, É., Monotonicity methods for white noise driven quasi-linear SPDEs (1990) Progr. Probab., 22, pp. 219-233. , Diffusion Processes and Related Problems in Analysis, Vol. I (Evanston, IL, 1989), Birkhäuser, Boston, Boston, MA 
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 
504 |a Cortázar, C., Elgueta, M., Unstability of the steady solution of a nonlinear reaction-diffusion equation (1991) Houston J. Math., 17 (2), pp. 149-155 
504 |a Dávila, J., Bonder, J.F., Rossi, J.D., Groisman, P., Sued, M., Numerical analysis of stochastic differential equations with explosions (2005) Stoch. Anal. Appl., 23 (4), pp. 809-825 
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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