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Topic · Applied Mathematics

Differential Equations and Boundary Problems

Differential Equations and Boundary Problems is a research topic within Applied Mathematics. Science Explorer counts 26k research works in it since 1950. 10.2% of them reached the world's top 10% most cited for their field and year.

This cluster of papers focuses on the study of nonlocal partial differential equations and boundary value problems, including topics such as solvability, numerical solutions, inverse problems, and the behavior of hyperbolic and parabolic equations with nonlocal conditions. The research also delves into the analysis of integro-differential equations and the properties of Green functions.

  • Nonlocal
  • Partial Differential Equations
  • Boundary Value Problems
  • Inverse Problem
  • Solvability
  • Numerical Solution
  • Hyperbolic Equations
  • Parabolic Equations
  • Integro-Differential Equations
  • Green Function
Research works
26k
fractional, since 1950
In the world top 10%
2.7k
per year above
Top-10% rate
10.2%
share of its works in the world top 10%
Growth, 2013–17 → 2018–22
+16%
the tick is no change

Which countries lead Differential Equations and Boundary Problems research?

By volume, Russia and China publish the most (747 and 467 works in 2022–2025).

By volume, 2022–2025

  1. 1 Russia 747 works
  2. 2 China 467 works
  3. 3 India 234 works
  4. 4 United States 178 works
  5. 5 Uzbekistan 178 works
  6. 6 Ukraine 161 works
  7. 7 Türkiye 137 works
  8. 8 Kazakhstan 128 works
  9. 9 Saudi Arabia 108 works
  10. 10 Italy 100 works

How concentrated that is

The same countries as shares of everything the list above accounts for. A node where two countries do two thirds of the work and one spread evenly across twelve read alike as a ranking and not at all alike here.

Russia: 30.7%China: 19.2%India: 9.6%United States: 7.3%6 others listed: 33.3%31%largest
Russia747 · 30.7%China467 · 19.2%India234 · 9.6%United States178 · 7.3%6 others listed812 · 33.3%

Shares of the rows listed above, not of the whole node.

Which institutions lead Differential Equations and Boundary Problems research?

By volume in 2022–2025, Lomonosov Moscow State University publishes the most Differential Equations and Boundary Problems research, followed by Institute of Mathematics and Mathematical Modeling and Academy of Sciences Republic of Uzbekistan.

By volume, 2022–2025

  1. 1 Lomonosov Moscow State UniversityRussia 78 works
  2. 2 Institute of Mathematics and Mathematical ModelingKazakhstan 40 works
  3. 3 Academy of Sciences Republic of UzbekistanUzbekistan 36 works
  4. 4 Peoples' Friendship University of RussiaRussia 31 works
  5. 5 Russian Academy of SciencesRussia 29 works
  6. 6 National University of UzbekistanUzbekistan 28 works
  7. 7 Université Sultan Moulay SlimaneMorocco 26 works
  8. 8 St Petersburg UniversityRussia 25 works
  9. 9 Baku State UniversityAzerbaijan 23 works
  10. 10 Belgorod National Research UniversityRussia 22 works

Who are the leading researchers in Differential Equations and Boundary Problems?

The most-cited researchers publishing on Differential Equations and Boundary Problems include Stanley Osher, Louis Nirenberg and Ivo Babuška.

  1. 1 Stanley Osher United States 8k citations
  2. 2 Louis Nirenberg United States 2.9k citations
  3. 3 Ivo Babuška United States 2.7k citations
  4. 4 Dumitru Bǎleanu Türkiye 2.2k citations
  5. 5 Peter D. Lax United States 2k citations

Ranked by citations received across their whole record, among researchers with at least three works on this topic.

Where is Differential Equations and Boundary Problems research done?

The largest centres of Differential Equations and Boundary Problems research in 2022–2025 are Moscow (Russia), Tashkent (Uzbekistan), Baku (Azerbaijan) and Almaty (Kazakhstan). Among places with at least 20 works in it, it is an unusually large share of all research in Beni Mellal, Bukhara and Chelyabinsk.

Largest cities, 2022–2025

  1. 1 Moscow Russia 269 works
  2. 2 Tashkent Uzbekistan 102 works
  3. 3 Baku Azerbaijan 78 works
  4. 4 Almaty Kazakhstan 72 works
  5. 5 Kyiv Ukraine 58 works
  6. 6 Beijing China 52 works
  7. 7 Novosibirsk Russia 39 works
  8. 8 Chelyabinsk Russia 36 works
  9. 9 Saint Petersburg Russia 35 works
  10. 10 Riyadh Saudi Arabia 33 works

Where it is the local speciality

  1. Beni MellalMA · 25.8 works49×
  2. BukharaUZ · 22.1 works41×
  3. ChelyabinskRU · 36.4 works40×
  4. BelgorodRU · 23.3 works40×
← less than its size predicts1×more →

Location quotient: how much more of its research is in Differential Equations and Boundary Problems than the world average.

See Differential Equations and Boundary Problems on the map

Where is the best place to study Differential Equations and Boundary Problems?

Among universities, judged by research, Université Sultan Moulay Slimane, Lomonosov Moscow State University and Qassim University score highest, combining excellence, specialisation, size, growth and international reach. Research strength is one signal when choosing where to study; it does not measure teaching.

0%20%40%mean 17.18%fractional works in this node (log) →share in the world top 10% →Université Sultan Moulay Slimane: 26, 29.9%Lomonosov Moscow State University: 78, 11.8%Qassim University: 10, 26.3%Al-Farabi Kazakh National University: 17, 13.4%South Ural State University: 16, 14.4%National University of Uzbekistan: 28, 11.8%Belgorod National Research University: 22, 9.6%Peoples' Friendship University of Russia: 31, 10.7%Tashkent State University of Economics: 8, 31.0%Sidi Mohamed Ben Abdellah University: 12, 12.9%Université Sultan Mo…Qassim UniversityAl-Farabi Kazakh Nat…Lomonosov Moscow Sta…
above the meannear itbelow it

One dot per university in the table below. The upper left is the interesting corner: small places doing unusually strong work.

#UniversityScoreTop 10%SpecialisationWorksGrowth
1 Université Sultan Moulay SlimaneMorocco 64.129.9%48.9×26 —
2 Lomonosov Moscow State UniversityRussia 63.711.8%23.9×78 +60.5%
3 Qassim UniversitySaudi Arabia 59.726.3%10.4×10 +95.5%
4 Al-Farabi Kazakh National UniversityKazakhstan 59.113.4%23.8×17 +642.6%
5 South Ural State UniversityRussia 58.014.4%35.0×16 +197.7%
6 National University of UzbekistanUzbekistan 57.711.8%48.5×28 +138.0%
7 Belgorod National Research UniversityRussia 56.69.6%65.4×22 +245.4%
8 Peoples' Friendship University of RussiaRussia 55.710.7%25.4×31 +108.6%
9 Tashkent State University of EconomicsUzbekistan 55.131.0%18.1×8 —
10 Sidi Mohamed Ben Abdellah UniversityMorocco 54.412.9%12.0×12 +547.2%

Universities only. Score blends excellence (30%), specialisation (25%), size (20%), growth (15%) and international reach (10%), 2015–2022; growth compares 2010–14 with 2015–19.

Is Differential Equations and Boundary Problems research growing?

Output in 2018–2022 was 16% higher than in 2013–2017, peaking in 2024. The fastest-growing topics are Differential Equations and Boundary Problems.

19801990200020102020
grewheldshrank

The same series as a ribbon — one cell per year, darker for more. The line above answers how much; this answers when.

Which topics inside it are moving

Growth and decline on one axis around a shared zero. Two lists side by side hide the thing that matters: whether the growth dwarfs the decline, or the other way round.