L. E. Payne

11.1k total citations · 1 hit paper
282 papers, 7.7k citations indexed

About

L. E. Payne is a scholar working on Computational Theory and Mathematics, Applied Mathematics and Mathematical Physics. According to data from OpenAlex, L. E. Payne has authored 282 papers receiving a total of 7.7k indexed citations (citations by other indexed papers that have themselves been cited), including 154 papers in Computational Theory and Mathematics, 115 papers in Applied Mathematics and 83 papers in Mathematical Physics. Recurrent topics in L. E. Payne's work include Advanced Mathematical Modeling in Engineering (140 papers), Nonlinear Partial Differential Equations (55 papers) and Numerical methods in inverse problems (51 papers). L. E. Payne is often cited by papers focused on Advanced Mathematical Modeling in Engineering (140 papers), Nonlinear Partial Differential Equations (55 papers) and Numerical methods in inverse problems (51 papers). L. E. Payne collaborates with scholars based in United States, United Kingdom and Canada. L. E. Payne's co-authors include Hans F. Weinberger, R. J. Knops, D. H. Sattinger, Brian Straughan, G. A. Philippin, Philip Schaefer, Junqiang Song, Howard A. Levine, Cornelius O. Horgan and William H. Pell and has published in prestigious journals such as Journal of Applied Physics, Journal of Fluid Mechanics and Brain Research.

In The Last Decade

L. E. Payne

269 papers receiving 6.5k citations

Hit Papers

Saddle points and instability of nonlinear hyperbolic equ... 1975 2026 1992 2009 1975 200 400 600
What are hit papers?

Hit papers significantly outperform the citation benchmark for their cohort. A paper qualifies if it has ≥500 total citations, achieves ≥1.5× the top-1% citation threshold for papers in the same subfield and year (this is the minimum needed to enter the top 1%, not the average within it), or reaches the top citation threshold in at least one of its specific research topics.

  1. Saddle points and instability of nonlinear hyperbolic equations
    1975 610 citations L. E. Payne et al. profile →

Peers — A (Enhanced Table)

Peers by citation overlap · career bar shows stage (early→late) cites · hero ref

Name h Career Trend Papers Cites
L. E. Payne United States 44 3.8k 3.2k 2.7k 1.6k 1.6k 282 7.7k
Alexander Mielke Germany 44 1.9k 0.5× 867 0.3× 644 0.2× 659 0.4× 1.8k 1.2× 195 5.7k
C. W. Groetsch United States 19 570 0.2× 569 0.2× 1.2k 0.5× 406 0.2× 420 0.3× 73 2.6k
Daniela Calvetti United States 32 989 0.3× 458 0.1× 775 0.3× 781 0.5× 231 0.1× 178 3.8k
Peter W. Jones United States 31 773 0.2× 3.7k 1.2× 1.9k 0.7× 273 0.2× 101 0.1× 73 5.1k
Habib Ammari France 39 1.4k 0.4× 254 0.1× 2.7k 1.0× 508 0.3× 2.2k 1.4× 283 6.3k
Alfred Gray United States 43 346 0.1× 2.4k 0.8× 620 0.2× 978 0.6× 122 0.1× 124 7.0k
Peter Kuchment United States 26 725 0.2× 254 0.1× 1.4k 0.5× 116 0.1× 771 0.5× 68 3.2k
G. Rodríguez United States 30 335 0.1× 338 0.1× 454 0.2× 258 0.2× 136 0.1× 132 2.6k
Michael Spivak United States 5 276 0.1× 731 0.2× 394 0.1× 337 0.2× 104 0.1× 9 2.4k
William C. Troy United States 29 413 0.1× 573 0.2× 408 0.2× 307 0.2× 38 0.0× 98 2.8k

Countries citing papers authored by L. E. Payne

Since Specialization
Citations

This map shows the geographic impact of L. E. Payne's research. It shows the number of citations coming from papers published by authors working in each country. You can also color the map by specialization and compare the number of citations received by L. E. Payne with the expected number of citations based on a country's size and research output (numbers larger than one mean the country cites L. E. Payne more than expected).

Fields of papers citing papers by L. E. Payne

Since Specialization
Physical SciencesHealth SciencesLife SciencesSocial Sciences

This network shows the impact of papers produced by L. E. Payne. Nodes represent research fields, and links connect fields that are likely to share authors. Colored nodes show fields that tend to cite the papers produced by L. E. Payne. The network helps show where L. E. Payne may publish in the future.

Co-authorship network of co-authors of L. E. Payne

This figure shows the co-authorship network connecting the top 25 collaborators of L. E. Payne. A scholar is included among the top collaborators of L. E. Payne based on the total number of citations received by their joint publications. Widths of edges represent the number of papers authors have co-authored together. Node borders signify the number of papers an author published with L. E. Payne. L. E. Payne is excluded from the visualization to improve readability, since they are connected to all nodes in the network.

All Works

20 of 20 papers shown
1.
Payne, L. E. & Junqiang Song. (2011). Lower bounds for blow-up in a model of chemotaxis. Journal of Mathematical Analysis and Applications. 385(2). 672–676. 27 indexed citations
2.
Payne, L. E. & Junqiang Song. (2009). Blow-up and decay criteria for a model of chemotaxis. Journal of Mathematical Analysis and Applications. 367(1). 1–6. 7 indexed citations
3.
Payne, L. E. & Junqiang Song. (2009). Lower bounds for blow-up time in a nonlinear parabolic problem. Journal of Mathematical Analysis and Applications. 354(1). 394–396. 48 indexed citations
4.
Payne, L. E. & Philip Schaefer. (2008). Blow-up in parabolic problems under Robin boundary conditions. Applicable Analysis. 87(6). 699–707. 27 indexed citations
5.
Fleck, Jessica I., Deborah L. Green, Jennifer L. Stevenson, et al.. (2008). The transliminal brain at rest: Baseline EEG, unusual experiences, and access to unconscious mental activity. Cortex. 44(10). 1353–1363. 28 indexed citations
6.
Payne, L. E. & Junqiang Song. (2007). Spatial decay bounds for double diffusive convection in Brinkman flow. Journal of Differential Equations. 244(2). 413–430. 10 indexed citations
7.
Payne, L. E. & Junqiang Song. (2007). Lower bounds for the blow-up time in a temperature dependent Navier–Stokes flow. Journal of Mathematical Analysis and Applications. 335(1). 371–376. 14 indexed citations
8.
Payne, L. E. & Philip Schaefer. (2006). Lower bounds for blow-up time in parabolic problems under Dirichlet conditions. Journal of Mathematical Analysis and Applications. 328(2). 1196–1205. 98 indexed citations
9.
Payne, L. E., et al.. (2006). Structural stability for the Brinkman equations of flow in double diffusive convection. Journal of Mathematical Analysis and Applications. 325(2). 1479–1490. 26 indexed citations
10.
Payne, L. E. & Junqiang Song. (2006). Spatial decay in a double diffusive convection problem in Darcy flow. Journal of Mathematical Analysis and Applications. 330(2). 864–875. 12 indexed citations
11.
Ames, Karen A., L. E. Payne, & Junqiang Song. (2005). On two classes of nonstandard parabolic problems. Journal of Mathematical Analysis and Applications. 311(1). 254–267. 5 indexed citations
12.
Ames, Karen A., L. E. Payne, & Philip Schaefer. (2004). Energy and pointwise bounds in some non-standard parabolic problems. Proceedings of the Royal Society of Edinburgh Section A Mathematics. 134(1). 1–9. 28 indexed citations
13.
Payne, L. E. & G. A. Philippin. (2004). Decay Bounds for Solutions of Second Order Parabolic Problems and their Derivatives III. Zeitschrift für Analysis und ihre Anwendungen. 23(4). 809–818. 7 indexed citations
14.
Payne, L. E., Philip Schaefer, & Junqiang Song. (2004). Improved bounds for some nonstandard problems in generalized heat conduction. Journal of Mathematical Analysis and Applications. 298(1). 325–340. 6 indexed citations
15.
Dassios, George & L. E. Payne. (1989). Energy bounds for Rayleigh scattering by an elastic cavity. Journal of Mathematical Analysis and Applications. 138(1). 106–128. 2 indexed citations
16.
Galdi, Giovanni P., L. E. Payne, M. R. E. Proctor, & Brian Straughan. (1987). Convection in thawing subsea permafrost. Proceedings of the Royal Society of London A Mathematical and Physical Sciences. 414(1846). 83–102. 24 indexed citations
17.
Horgan, Cornelius O. & L. E. Payne. (1984). Decay estimates for second-order quasilinear partial differential equations. Advances in Applied Mathematics. 5(3). 309–332. 34 indexed citations
18.
Horgan, Cornelius O. & L. E. Payne. (1984). Decay estimates for a class of second-order quasilinear equations in three dimensions. Archive for Rational Mechanics and Analysis. 86(3). 279–289. 21 indexed citations
19.
Payne, L. E. & D. Sather. (1967). On Some Improperly Posed Problems for Quasilinear Equations of Mixed Type. Transactions of the American Mathematical Society. 128(1). 135–135. 2 indexed citations
20.
Payne, L. E.. (1956). Multivalued functions in generalized axially symmetric potential theory. French digital mathematics library (Numdam). 10. 135–145.

Rankless uses publication and citation data sourced from OpenAlex, an open and comprehensive bibliographic database. While OpenAlex provides broad and valuable coverage of the global research landscape, it—like all bibliographic datasets—has inherent limitations. These include incomplete records, variations in author disambiguation, differences in journal indexing, and delays in data updates. As a result, some metrics and network relationships displayed in Rankless may not fully capture the entirety of a scholar's output or impact.

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