{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,8]],"date-time":"2025-07-08T04:04:36Z","timestamp":1751947476057,"version":"3.41.2"},"reference-count":14,"publisher":"Springer Science and Business Media LLC","issue":"1-3","license":[{"start":{"date-parts":[[1997,4,1]],"date-time":"1997-04-01T00:00:00Z","timestamp":859852800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[1997,4,1]],"date-time":"1997-04-01T00:00:00Z","timestamp":859852800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numerical Algorithms"],"published-print":{"date-parts":[[1997,4]]},"DOI":"10.1023\/a:1019117130906","type":"journal-article","created":{"date-parts":[[2003,2,19]],"date-time":"2003-02-19T23:30:27Z","timestamp":1045697427000},"page":"211-225","source":"Crossref","is-referenced-by-count":1,"title":["Numerical bifurcation and stability analysis for steady-states of reaction diffusion equations"],"prefix":"10.1007","volume":"14","author":[{"given":"M. W.","family":"Smiley","sequence":"first","affiliation":[]}],"member":"297","reference":[{"key":"329186_CR1","first-page":"1","volume-title":"Nonlinear Functional Analysis and Differential Equations","author":"L. Cesari","year":"1976","unstructured":"L. Cesari, Functional analysis, nonlinear differential equations, and the alternative method, in: Nonlinear Functional Analysis and Differential Equations, eds. Cesari, Kannan and Schuur (Marcel Dekker, New York, 1976) pp. 1\u2013197."},{"key":"329186_CR2","volume-title":"Methods of Bifurcation Theory","author":"S.-N. Chow","year":"1983","unstructured":"S.-N. Chow and J. K. Hale, Methods of Bifurcation Theory (Springer, New York, 1983)."},{"key":"329186_CR3","doi-asserted-by":"crossref","unstructured":"P. Ciarlet, The Finite Element Method for Elliptic Problems (North-Holland, Amsterdam, 1978).","DOI":"10.1115\/1.3424474"},{"issue":"IV","key":"329186_CR4","first-page":"29","volume":"5","author":"C. Foias","year":"1978","unstructured":"C. Foias and R. Temam, \u2014Remarques sur les \u00e9quations de Navier-Stokes stationnaires et les ph\u00e9nom\u00e8nes successifs de bifurcation, Ann. Scuola Norm Sup.-Pisa 5(IV) (1978) 29\u201363.","journal-title":"Ann. Scuola Norm Sup.-Pisa"},{"key":"329186_CR5","volume-title":"Elliptic Partial Differential Equations of Second Order","author":"D. Gilbarg","year":"1983","unstructured":"D. Gilbarg and N. Trudinger, Elliptic Partial Differential Equations of Second Order (Springer, New York, 1983)."},{"key":"329186_CR6","doi-asserted-by":"crossref","unstructured":"J. K. Hale, Asymptotic Behavior of Dissipative Systems (Amer. Math. Soc., Providence, RI, 1988).","DOI":"10.1007\/978-3-642-86458-2_14"},{"key":"329186_CR7","doi-asserted-by":"crossref","DOI":"10.1007\/BFb0089647","volume-title":"Geometric Theory of Semilinear Parabolic Equations","author":"D. Henry","year":"1981","unstructured":"D. Henry, Geometric Theory of Semilinear Parabolic Equations (Springer, New York, 1981)."},{"key":"329186_CR8","doi-asserted-by":"publisher","first-page":"205","DOI":"10.1007\/BF01386407","volume":"57","author":"M. Marion","year":"1990","unstructured":"M. Marion and R. Temam, Nonlinear Galerkin methods - the finite element case, Numer. Math. 57 (1990) 205\u2013226.","journal-title":"Numer. Math."},{"key":"329186_CR9","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1080\/00036819308840194","volume":"50","author":"M. Smiley","year":"1993","unstructured":"M. Smiley, Global attractors and approximate inertial manifolds for nonautonomous dissipative equations, Applicable Analysis 50 (1993) 217\u2013241.","journal-title":"Applicable Analysis"},{"key":"329186_CR10","doi-asserted-by":"publisher","first-page":"311","DOI":"10.1016\/0377-0427(95)00208-1","volume":"70","author":"M. Smiley","year":"1996","unstructured":"M. Smiley, A finite element method for computing the bifurcation function for semilinear elliptic BVP's, J. Comp. Appl. Math. 70 (1996) 311\u2013327.","journal-title":"J. Comp. Appl. Math."},{"key":"329186_CR11","unstructured":"M. Smiley, A global version of the principle of reduced stability, Preprint to appear."},{"key":"329186_CR12","volume-title":"An Analysis of the Finite Element Method","author":"G. Strang","year":"1973","unstructured":"G. Strang and G. Fix, An Analysis of the Finite Element Method (Prentice-Hall, Englewood Cliffs, NJ, 1973)."},{"key":"329186_CR13","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4684-0313-8","volume-title":"Infinite-Dimensional Dynamical Systems in Mechanics and Physics","author":"R. Temam","year":"1988","unstructured":"R. Temam, Infinite-Dimensional Dynamical Systems in Mechanics and Physics (Springer, New York, 1988)."},{"key":"329186_CR14","doi-asserted-by":"publisher","first-page":"540","DOI":"10.1016\/0022-247X(90)90061-J","volume":"149","author":"E. Titi","year":"1990","unstructured":"E. Titi, On approximate inertial manifolds to the Navier-Stokes equations, J. Math. Anal. Appl. 149 (1990) 540\u2013557.","journal-title":"J. Math. Anal. Appl."}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1019117130906.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1023\/A:1019117130906\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1019117130906.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,7]],"date-time":"2025-07-07T06:45:58Z","timestamp":1751870758000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1023\/A:1019117130906"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1997,4]]},"references-count":14,"journal-issue":{"issue":"1-3","published-print":{"date-parts":[[1997,4]]}},"alternative-id":["329186"],"URL":"https:\/\/doi.org\/10.1023\/a:1019117130906","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"type":"print","value":"1017-1398"},{"type":"electronic","value":"1572-9265"}],"subject":[],"published":{"date-parts":[[1997,4]]}}}