Shadowing para Aproximar la Solución de problemas Parabólicos Semilineales para intervalos de Tiempo Grandes.


  • Ulices Zavaleta Calderón
  • Nelson Aragonéz Salazar
  • Roxana Rodríguez



difusión-reacción, simulación, reacción


Se presenta un resultado de shadowing para un problema de evolucion parabolico no autonomo. Utilizando el metodo de Euler hacia atras se demuestra que bajo ciertas hipótesis de regularidad se puede aproximar usando shadowing la solucion de un problema de la forma
                               u'(t) = A(t)u(t) + f(t);
donde A(t) es el generador de un semigrupo analítico sobre un espacio de Banach.


J.L. Dautray, R. and Lions, Mathematical analysis and numerical methods for sciences and technology, vol. 5, Springer-Verlag, Berlin, 1990.

S. Elliott, CH. and Larson, A nite element model for the time-dependent joule heating problem, Math. Comp. 64 (1995), no. 212, 1433-1453.

Q. Fang, Inertial manifold theory for a class of reaction-diusion equations on thin tubular domains, Hirshima Math. J. 23 (1993), no. 3, 459-508.

A. Palencia C. and Thalhammer M. Gonzalez, C. Ostermann, Backward euler discretization of fully nonlinear parabolic problems, Math. Comp.

C. Gonzalez, C. and Palencia, Stability of time stepping methods for abstract time dependent parabolic problems, SIAM J. Anal. 35 (1998), 973-989.

W. Hayes, Rigorous shadowing of numerical solutions of ordinary diferential equations by containment, Doctors thesis., University of Toronto, Graduate Departament of Computer Sciences, 2001.

D. Henry, Geometric theory of semilinear parabolics equations, vol. 840, Springer-Verlag, 1981.

J. M. Larson, S. and Sanz-Serna, A shadowing result with applications to nite element approximation of reaction-diusion equations, Mathematics of Computation 68 (1999), no. 225, 55-72.

S.Y Larson, S. and Pilyugin, Numerical shadowing near the global attractor for a semilinear parabolic equation, Preprint.

J.D. Mimura, M. and Murray, Prey-predator model which exibits patchiness, J. Theor. Biol. 75 (1979), 249-262.

C. Ostermann, A. and Palencia, Shadowing for nonautonomous parabolic problems with applications to long-time error bounds, SIAM J. Numer. Anal. 37 (2000), no. 5, 1399-1419.

A. Pazy, Semigroups of linear operators and applications to partial dierential equations, Springer-Verlag, New York, 1983.

S. Pilyugin, Shadowing in dynamical systems, vol. 1706, Springer-Verlag, 1999.

J. Smoller, Shock waves and reaction-diusion equations, Springer-Verlag, New-York, 1983.

A.M. Stuart and A.R Humphries, Dyamical systems and numerical analysis, Cambridge University Press, New York, 1996.

H. Tanabe, Equation of evolution, Pitman, London, 1979.

R. Temam, Innite-dimensional dynamical systems in mechanics and physics, Springer-Verlag, New York, 1988.



How to Cite

Zavaleta Calderón, U., Aragonéz Salazar, N., & Rodríguez, R. (2015). Shadowing para Aproximar la Solución de problemas Parabólicos Semilineales para intervalos de Tiempo Grandes. Selecciones Matemáticas, 1(01).

Most read articles by the same author(s)