Philip Schaefer

1.6k total citations
79 papers, 1.1k citations indexed

About

Philip Schaefer is a scholar working on Computational Theory and Mathematics, Applied Mathematics and Mathematical Physics. According to data from OpenAlex, Philip Schaefer has authored 79 papers receiving a total of 1.1k indexed citations (citations by other indexed papers that have themselves been cited), including 33 papers in Computational Theory and Mathematics, 30 papers in Applied Mathematics and 26 papers in Mathematical Physics. Recurrent topics in Philip Schaefer's work include Advanced Mathematical Modeling in Engineering (33 papers), Differential Equations and Boundary Problems (16 papers) and Nonlinear Partial Differential Equations (15 papers). Philip Schaefer is often cited by papers focused on Advanced Mathematical Modeling in Engineering (33 papers), Differential Equations and Boundary Problems (16 papers) and Nonlinear Partial Differential Equations (15 papers). Philip Schaefer collaborates with scholars based in United States, Germany and South Korea. Philip Schaefer's co-authors include L. E. Payne, G. A. Philippin, Markus Gampert, Karen A. Ames, Nils Peters, Norbert Peters, R. Sperb, Junqiang Song, Chris Cosner and Venkateswaran Narayanaswamy and has published in prestigious journals such as Journal of Fluid Mechanics, Physics of Fluids and Journal of Mathematical Analysis and Applications.

In The Last Decade

Philip Schaefer

75 papers receiving 992 citations

Peers — A (Enhanced Table)

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

Name h Career Trend Papers Cites
Philip Schaefer United States 19 631 518 374 233 221 79 1.1k
George E. Trapp United States 12 264 0.4× 472 0.9× 100 0.3× 153 0.7× 63 0.3× 31 908
Giles Auchmuty United States 19 287 0.5× 419 0.8× 186 0.5× 203 0.9× 93 0.4× 56 854
Robert Sharpley United States 14 572 0.9× 152 0.3× 281 0.8× 192 0.8× 118 0.5× 46 1.1k
В. А. Галактионов Russia 14 256 0.4× 161 0.3× 211 0.6× 151 0.6× 189 0.9× 132 844
Alfred S. Carasso United States 17 164 0.3× 220 0.4× 455 1.2× 237 1.0× 60 0.3× 58 938
René Pinnau Germany 17 249 0.4× 124 0.2× 277 0.7× 424 1.8× 69 0.3× 77 861
Carlos S. Kubrusly Brazil 15 349 0.6× 181 0.3× 311 0.8× 47 0.2× 321 1.5× 85 933
Ulrich Tautenhahn Germany 23 423 0.7× 330 0.6× 1.2k 3.3× 314 1.3× 49 0.2× 44 1.4k
Geneviève Raugel France 18 512 0.8× 604 1.2× 375 1.0× 354 1.5× 825 3.7× 39 1.3k
P. J. Laurent France 10 177 0.3× 297 0.6× 98 0.3× 336 1.4× 60 0.3× 19 858

Countries citing papers authored by Philip Schaefer

Since Specialization
Citations

This map shows the geographic impact of Philip Schaefer'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 Philip Schaefer with the expected number of citations based on a country's size and research output (numbers larger than one mean the country cites Philip Schaefer more than expected).

Fields of papers citing papers by Philip Schaefer

Since Specialization
Physical SciencesHealth SciencesLife SciencesSocial Sciences

This network shows the impact of papers produced by Philip Schaefer. 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 Philip Schaefer. The network helps show where Philip Schaefer may publish in the future.

Co-authorship network of co-authors of Philip Schaefer

This figure shows the co-authorship network connecting the top 25 collaborators of Philip Schaefer. A scholar is included among the top collaborators of Philip Schaefer 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 Philip Schaefer. Philip Schaefer 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.
Gampert, Markus, Venkateswaran Narayanaswamy, Philip Schaefer, & Norbert Peters. (2013). Conditional statistics of the turbulent/non-turbulent interface in a jet flow. Journal of Fluid Mechanics. 731. 615–638. 26 indexed citations
2.
Schaefer, Philip. (2009). BLOW-UP PHENOMENA IN SOME POROUS MEDIUM PROBLEMS. Dynamic Systems and Applications. 18. 7 indexed citations
3.
Payne, L. E. & Philip Schaefer. (2008). Blow-up in parabolic problems under Robin boundary conditions. Applicable Analysis. 87(6). 699–707. 27 indexed citations
4.
Schaefer, Philip, et al.. (2007). On a conjecture for an overdetermined problem for the biharmonic operator. Applied Mathematics Letters. 21(4). 421–424. 2 indexed citations
5.
Payne, L. E., G. A. Philippin, & Philip Schaefer. (2007). Bounds for blow-up time in nonlinear parabolic problems. Journal of Mathematical Analysis and Applications. 338(1). 438–447. 46 indexed citations
6.
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
7.
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
8.
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
9.
Payne, L. E. & Philip Schaefer. (2002). Energy bounds for some nonstandard problems in partial differential equations. Journal of Mathematical Analysis and Applications. 273(1). 75–92. 18 indexed citations
10.
Schaefer, Philip, et al.. (2002). On Solutions of. Journal of Inequalities and Applications. 2002(4). 325650–325650. 34 indexed citations
11.
Payne, L. E. & Philip Schaefer. (2001). Eigenvalue and eigenfunction inequalities for the elastically supported membrane. Zeitschrift für angewandte Mathematik und Physik. 52(5). 888–895. 4 indexed citations
12.
Payne, L. E. & Philip Schaefer. (1994). Some Phragm�n-Lindel�f type results for the biharmonic equation. Zeitschrift für angewandte Mathematik und Physik. 45(3). 414–432. 19 indexed citations
13.
Schaefer, Philip. (1991). Analytic solution of qualitative differential equations. National Conference on Artificial Intelligence. 830–835. 6 indexed citations
14.
Cosner, Chris & Philip Schaefer. (1989). Sign-definite solutions in some linear elliptic systems. Proceedings of the Royal Society of Edinburgh Section A Mathematics. 111(3-4). 347–358. 9 indexed citations
15.
Cosner, Chris & Philip Schaefer. (1987). A comparison principle for a class of fourth-order elliptic operators. Journal of Mathematical Analysis and Applications. 128(2). 488–494. 9 indexed citations
16.
Schaefer, Philip, et al.. (1987). Using Expert Systems to Troubleshoot Microprocessor-Based Control Systems: An Expectation-Based Approach *. IFAC Proceedings Volumes. 20(4). 95–98. 1 indexed citations
17.
Schaefer, Philip, et al.. (1981). On a subharmonic functional in fourth order nonlinear elliptic problems. Journal of Mathematical Analysis and Applications. 83(1). 20–25. 9 indexed citations
18.
Schaefer, Philip & Wolfgang Walter. (1979). On pointwise estimates for metaharmonic functions. Journal of Mathematical Analysis and Applications. 69(1). 171–179. 2 indexed citations
19.
Schaefer, Philip & R. Sperb. (1976). Maximum principles for some functionals associated with the solution of elliptic boundary value problems. Archive for Rational Mechanics and Analysis. 61(1). 65–76. 17 indexed citations
20.
Schaefer, Philip. (1971). On the Cauchy problem for the nonlinear biharmonic equation. Journal of Mathematical Analysis and Applications. 36(3). 660–673. 6 indexed citations

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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