Skip to main content
    • Aa
    • Aa



In this paper we provide a new proof of strong convergence of resolvent operators associated with boundary value problems on thin domains.

Corresponding author
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

J. M. Arrieta and A. N. Carvalho, ‘Spectral convergence and nonlinear dynamics of reaction–diffusion equations under perturbations of the domain’, J. Differential Equations 199 (2004), 143178.

J. M. Arrieta, A. N. Carvalho and G. Lozada-Cruz, ‘Dynamics in dumbbell domains I. Continuity of the set of equilibria’, J. Differential Equations 231 (2) (2006), 551597.

J. M. Arrieta, A. N. Carvalho and G. Lozada-Cruz, ‘Dynamics in dumbbell domains II. The limiting problem’, J. Differential Equations 247 (2009), 174202.

J. M. Arrieta, A. N. Carvalho, M. C. Pereira and R. P. Silva, ‘Semilinear parabolic problems in thin domains with a highly oscillatory boundary’, Nonlinear Anal. 74 (2011), 51115132.

V. L. Carbone, A. N. Carvalho and K. Schiabel-Silva, ‘Continuity of attractors for parabolic problems with localized large diffusion’, Nonlinear Anal. 68 (2008), 515535.

A. N. Carvalho and S. Piskarev, ‘A general approximation scheme for attractors of abstract parabolic problems’, Numer. Funct. Anal. Optim. 27 (7–8) (2006), 785829.

I. S. Ciuperca, ‘Reaction–diffusion equations on thin domains with varying order of thinness’, J. Differential Equations 126 (1996), 244291.

T. Elsken, ‘Attractors for reaction–diffusion equations on thin domains whose linear part is nonself-adjoint’, J. Differential Equations 206 (2004), 94126.

T. Elsken, ‘A reaction–diffusion equation on a net-shaped thin domain’, Studia Math. 165 (2004), 159199.

T. Elsken, ‘Continuity of attractors for net-shaped thin domain’, Topol. Methods Nonlinear Anal. 26 (2005), 315354.

M. Prizzi, M. Rinaldi and K. P. Rybakowski, ‘Curved thin domains and parabolic equations’, Studia Math. 151 (2002), 109140.

M. Prizzi and K. P. Rybakowski, ‘The effect of domain squeezing upon the dynamics of reaction–diffusion equations’, J. Differential Equations 173 (2001), 271320.

A. M. Rekalo, ‘Asymptotic behavior of solutions of nonlinear parabolic equations on two-layer thin domains’, Nonlinear Anal. 52 (2003), 13931410.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *