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Partial Differential Equations and Applications / Springer

Citation Profile [Updated: 2026-03-14 21:09:38]
5 Years H Index
4
Impact Factor (IF)
0.07
5 Years IF
0.05
Data available in this report

[Raw data] [50 most cited papers] [50 most relevant papers] [cites used to compute IF] [Recent citations ][Frequent citing series ] [more data in EconPapers] [trace new citations] [Missing citations? Add them now] [Incorrect content? Let us know]

Main indicators
Raw Data

 

IF AIF CIF IF5 DOC CDO CIT NCI CCU D2Y C2Y D5Y C5Y SC %SC CiY II AII
2020 0 0.64 0 0 49 49 18 0 0 0 0 0 0.3
2021 0 0.74 0.02 0 83 132 27 2 2 49 49 1 50 2 0.02 0.27
2022 0.08 0.73 0.07 0.08 82 214 14 14 16 132 11 132 11 0 2 0.02 0.22
2023 0.06 0.69 0.07 0.08 51 265 6 19 35 165 10 214 17 5 26.3 0 0.2
2024 0.04 0.81 0.05 0.05 35 300 0 16 51 133 5 265 14 4 25 0 0.23
2025 0.07 0.06 0.05 55 355 0 20 71 86 6 300 16 5 25 0
IF: Two years Impact Factor: C2Y / D2Y
AIF: Average Impact Factor for all series in RePEc in year y
CIF: Cumulative impact factor
IF5: Five years Impact Factor: C5Y / D5Y
DOC: Number of documents published in year y
CDO: Cumulative number of documents published until year y
CIT: Number of citations to papers published in year y
NCI: Number of citations in year y
CCU: Cumulative number of citations to papers published until year y
D2Y: Number of articles published in y-1 plus y-2
C2Y: Cites in y to articles published in y-1 plus y-2
D5Y: Number of articles published in y-1 until y-5
C5Y: Cites in y to articles published in y-1 until y-5
SC: selft citations in y to articles published in y-1 plus y-2
%SC: Percentage of selft citations in y to articles published in y-1 plus y-2
CiY: Cites in year y to documents published in year y
II: Immediacy Index: CiY / Documents.
AII: Average Immediacy Index for series in RePEc in year y
50 most cited documents in this series
#YearTitleCited
12020A proof that rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear heat equations. (2020). Nguyen, Tuan Anh ; Kruse, Thomas ; Hutzenthaler, Martin ; Jentzen, Arnulf. In: Partial Differential Equations and Applications. RePEc:spr:pardea:v:1:y:2020:i:2:d:10.1007_s42985-019-0006-9.

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15
22021Neural networks-based backward scheme for fully nonlinear PDEs. (2021). Warin, Xavier ; Germain, Maximilien ; Pham, Huyen. In: Partial Differential Equations and Applications. RePEc:spr:pardea:v:2:y:2021:i:1:d:10.1007_s42985-020-00062-8.

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11
32021Multilevel Picard iterations for solving smooth semilinear parabolic heat equations. (2021). , Weinan ; Kruse, Thomas ; Hutzenthaler, Martin ; Jentzen, Arnulf. In: Partial Differential Equations and Applications. RePEc:spr:pardea:v:2:y:2021:i:6:d:10.1007_s42985-021-00089-5.

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8
42022Eckhaus instability of stationary patterns in hyperbolic reaction–diffusion models on large finite domains. (2022). Consolo, Giancarlo ; Grifo, Gabriele. In: Partial Differential Equations and Applications. RePEc:spr:pardea:v:3:y:2022:i:5:d:10.1007_s42985-022-00193-0.

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4
52022Deep learning schemes for parabolic nonlocal integro-differential equations. (2022). Castro, Javier. In: Partial Differential Equations and Applications. RePEc:spr:pardea:v:3:y:2022:i:6:d:10.1007_s42985-022-00213-z.

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4
62023Solving Kolmogorov PDEs without the curse of dimensionality via deep learning and asymptotic expansion with Malliavin calculus. (2023). Yamada, Toshihiro ; Takahashi, Akihiko. In: Partial Differential Equations and Applications. RePEc:spr:pardea:v:4:y:2023:i:4:d:10.1007_s42985-023-00240-4.

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3
72021The unique continuation property for second order evolution PDEs. (2021). Choulli, Mourad. In: Partial Differential Equations and Applications. RePEc:spr:pardea:v:2:y:2021:i:5:d:10.1007_s42985-021-00123-6.

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3
82021Solving high-dimensional Hamilton–Jacobi–Bellman PDEs using neural networks: perspectives from the theory of controlled diffusions and measures on path space. (2021). Nusken, Nikolas ; Richter, Lorenz. In: Partial Differential Equations and Applications. RePEc:spr:pardea:v:2:y:2021:i:4:d:10.1007_s42985-021-00102-x.

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3
92022Deep neural network approximations for solutions of PDEs based on Monte Carlo algorithms. (2022). Grohs, Philipp ; Salimova, Diyora ; Jentzen, Arnulf. In: Partial Differential Equations and Applications. RePEc:spr:pardea:v:3:y:2022:i:4:d:10.1007_s42985-021-00100-z.

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2
102022Existence of a minimizer for a nonlinear Schrödinger system with three wave interaction under non-symmetric potentials. (2022). Osada, Yuki. In: Partial Differential Equations and Applications. RePEc:spr:pardea:v:3:y:2022:i:2:d:10.1007_s42985-022-00160-9.

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2
112022Blow up of solutions of semilinear wave equations related to nonlinear waves in de Sitter spacetime. (2022). Wakasugi, Yuta ; Tsutaya, Kimitoshi. In: Partial Differential Equations and Applications. RePEc:spr:pardea:v:3:y:2022:i:1:d:10.1007_s42985-021-00145-0.

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1
122023Higher-order error estimates for physics-informed neural networks approximating the primitive equations. (2023). Tang, Sui ; Hu, Ruimeng ; Lin, Quyuan ; Raydan, Alan. In: Partial Differential Equations and Applications. RePEc:spr:pardea:v:4:y:2023:i:4:d:10.1007_s42985-023-00254-y.

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1
132021Attraction–repulsion taxis mechanisms in a predator–prey model. (2021). Bell, Jonathan ; Haskell, Evan C. In: Partial Differential Equations and Applications. RePEc:spr:pardea:v:2:y:2021:i:3:d:10.1007_s42985-021-00080-0.

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1
142022Large time asymptotics for the fractional modified Korteweg-de Vries equation with $$\alpha \in \left( 2,4\right) $$ α ∈ 2 , 4. (2022). Naumkin, Pavel I ; Hayashi, Nakao ; Sanchez-Suarez, Isahi. In: Partial Differential Equations and Applications. RePEc:spr:pardea:v:3:y:2022:i:6:d:10.1007_s42985-022-00206-y.

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1
152020Global existence of solutions to some equations modeling phase separation of self-propelled particles. (2020). Bae, Hantaek. In: Partial Differential Equations and Applications. RePEc:spr:pardea:v:1:y:2020:i:6:d:10.1007_s42985-020-00047-7.

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1
162021Development and analysis of entropy stable no-slip wall boundary conditions for the Eulerian model for viscous and heat conducting compressible flows. (2021). Sayyari, Mohammed ; Parsani, Matteo ; Dalcin, Lisandro. In: Partial Differential Equations and Applications. RePEc:spr:pardea:v:2:y:2021:i:6:d:10.1007_s42985-021-00132-5.

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1
172021On the uniqueness of a suitable weak solution to the Navier–Stokes Cauchy problem. (2021). Maremonti, Paolo ; Crispo, Francesca. In: Partial Differential Equations and Applications. RePEc:spr:pardea:v:2:y:2021:i:3:d:10.1007_s42985-021-00073-z.

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1
182024Energy decay analysis for Porous elastic system with microtemperature: Classical vs second spectrum approach. (2024). Zougheib, Hamza ; el Arwadi, Toufic ; El-Hindi, Mohammad ; Soufyane, Abdelaziz. In: Partial Differential Equations and Applications. RePEc:spr:pardea:v:5:y:2024:i:2:d:10.1007_s42985-024-00273-3.

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1
192020Stability analysis of a delayed sir epidemic model with diffusion and saturated incidence rate. (2020). Boutayeb, Salahaddine ; Rachik, Mostafa ; Laarabi, Hassan ; Alaoui, Hamad Talibi ; Abta, Abdelhadi. In: Partial Differential Equations and Applications. RePEc:spr:pardea:v:1:y:2020:i:4:d:10.1007_s42985-020-00015-1.

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1
202023Global logarithmic stability of a Cauchy problem for anisotropic wave equations. (2023). Choulli, Mourad ; Bellassoued, Mourad. In: Partial Differential Equations and Applications. RePEc:spr:pardea:v:4:y:2023:i:3:d:10.1007_s42985-023-00242-2.

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1
212021An alternative proof of $$L^q$$ L q – $$L^r$$ L r estimates of the Oseen semigroup in higher dimensional exterior domains. (2021). Hishida, Toshiaki. In: Partial Differential Equations and Applications. RePEc:spr:pardea:v:2:y:2021:i:2:d:10.1007_s42985-021-00086-8.

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1
222023Neural networks for first order HJB equations and application to front propagation with obstacle terms. (2023). Warin, Xavier ; Bokanowski, Olivier ; Prost, Averil. In: Partial Differential Equations and Applications. RePEc:spr:pardea:v:4:y:2023:i:5:d:10.1007_s42985-023-00258-8.

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1
232020Asymptotic behavior for a class of derivative nonlinear Schrödinger systems. (2020). Katayama, Soichiro ; Sakoda, Daisuke. In: Partial Differential Equations and Applications. RePEc:spr:pardea:v:1:y:2020:i:3:d:10.1007_s42985-020-00012-4.

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1
242023A deep learning approach to the probabilistic numerical solution of path-dependent partial differential equations. (2023). Privault, Nicolas ; Yu, Jiang. In: Partial Differential Equations and Applications. RePEc:spr:pardea:v:4:y:2023:i:4:d:10.1007_s42985-023-00255-x.

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1
252022Local existence for the non-resistive magnetohydrodynamic system with fractional dissipation in the $$L^p$$ L p framework. (2022). Yao, Zheng-An ; Qiu, Hua. In: Partial Differential Equations and Applications. RePEc:spr:pardea:v:3:y:2022:i:6:d:10.1007_s42985-022-00211-1.

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1
262020Fourth-order time-stepping compact finite difference method for multi-dimensional space-fractional coupled nonlinear Schrödinger equations. (2020). Almushaira, Mustafa ; Liu, Fei. In: Partial Differential Equations and Applications. RePEc:spr:pardea:v:1:y:2020:i:6:d:10.1007_s42985-020-00048-6.

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1
50 most relevant documents in this series (papers most cited in the last two years)
#YearTitleCited
12021Multilevel Picard iterations for solving smooth semilinear parabolic heat equations. (2021). , Weinan ; Kruse, Thomas ; Hutzenthaler, Martin ; Jentzen, Arnulf. In: Partial Differential Equations and Applications. RePEc:spr:pardea:v:2:y:2021:i:6:d:10.1007_s42985-021-00089-5.

Full description at Econpapers || Download paper

4
22021Neural networks-based backward scheme for fully nonlinear PDEs. (2021). Warin, Xavier ; Germain, Maximilien ; Pham, Huyen. In: Partial Differential Equations and Applications. RePEc:spr:pardea:v:2:y:2021:i:1:d:10.1007_s42985-020-00062-8.

Full description at Econpapers || Download paper

4
32020A proof that rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear heat equations. (2020). Nguyen, Tuan Anh ; Kruse, Thomas ; Hutzenthaler, Martin ; Jentzen, Arnulf. In: Partial Differential Equations and Applications. RePEc:spr:pardea:v:1:y:2020:i:2:d:10.1007_s42985-019-0006-9.

Full description at Econpapers || Download paper

4
42023Solving Kolmogorov PDEs without the curse of dimensionality via deep learning and asymptotic expansion with Malliavin calculus. (2023). Yamada, Toshihiro ; Takahashi, Akihiko. In: Partial Differential Equations and Applications. RePEc:spr:pardea:v:4:y:2023:i:4:d:10.1007_s42985-023-00240-4.

Full description at Econpapers || Download paper

3
52022Existence of a minimizer for a nonlinear Schrödinger system with three wave interaction under non-symmetric potentials. (2022). Osada, Yuki. In: Partial Differential Equations and Applications. RePEc:spr:pardea:v:3:y:2022:i:2:d:10.1007_s42985-022-00160-9.

Full description at Econpapers || Download paper

2
62021The unique continuation property for second order evolution PDEs. (2021). Choulli, Mourad. In: Partial Differential Equations and Applications. RePEc:spr:pardea:v:2:y:2021:i:5:d:10.1007_s42985-021-00123-6.

Full description at Econpapers || Download paper

2
72021Solving high-dimensional Hamilton–Jacobi–Bellman PDEs using neural networks: perspectives from the theory of controlled diffusions and measures on path space. (2021). Nusken, Nikolas ; Richter, Lorenz. In: Partial Differential Equations and Applications. RePEc:spr:pardea:v:2:y:2021:i:4:d:10.1007_s42985-021-00102-x.

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2
82022Deep learning schemes for parabolic nonlocal integro-differential equations. (2022). Castro, Javier. In: Partial Differential Equations and Applications. RePEc:spr:pardea:v:3:y:2022:i:6:d:10.1007_s42985-022-00213-z.

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2
Citing documents used to compute impact factor: 6
YearTitle
2025Asymptotic Expansions as Control Variates for Deep Solvers to Fully-coupled Forward-backward Stochastic Differential Equations Abstract Coupled forward-backward stochastic differential equations (FBSDEs) are closely related to financially important issues such as optimal investment. However, it is well known that obtaining solutions is challenging, even when employing numerical methods. In this paper, we propose new methods that combine an algorithm recently developed for coupled FBSDEs and an asymptotic expansion approach to those FBSDEs as control variates for learning of the neural networks. The proposed method is demonstrated to perform better than the original algorithm in numerical examples, including one with a financial implication. The results show that the proposed method exhibits not only faster convergence but also greater stability in computation.. (2025). Naito, Makoto ; Saito, Taiga ; Takahashi, Akihiko ; Takehara, Kohta. In: CIRJE F-Series. RePEc:tky:fseres:2025cf1245.

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2025Asymptotic expansions as control variates for deep solvers to fully-coupled forward-backward stochastic differential equations Forthcoming in PLOS ONE. (2025). Saito, Taiga ; Naito, Makoto ; Takahashi, Akihiko ; Takehara, Kohta. In: CARF F-Series. RePEc:cfi:fseres:cf600.

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2025Full error analysis of the random deep splitting method for nonlinear parabolic PDEs and PIDEs. (2025). Wu, Sizhou ; Schmocker, Philipp ; Neufeld, Ariel. In: Papers. RePEc:arx:papers:2405.05192.

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2025Data-driven fractional algebraic system solver. (2025). Lorin, Emmanuel ; Nhan, Howl. In: Mathematics and Computers in Simulation (MATCOM). RePEc:eee:matcom:v:236:y:2025:i:c:p:170-182.

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2025Representation Results and Error Estimates for Differential Games with Applications Using Neural Networks. (2025). Warin, Xavier ; Bokanowski, Olivier. In: Dynamic Games and Applications. RePEc:spr:dyngam:v:15:y:2025:i:2:d:10.1007_s13235-024-00597-0.

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2025Well-posedness and decay of the energy of the viscoelastic porous elastic system with dual phase-lag model. (2025). Wang, Teng ; Zhou, Jun. In: Mathematics and Computers in Simulation (MATCOM). RePEc:eee:matcom:v:234:y:2025:i:c:p:262-285.

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Recent citations
Recent citations received in 2023
YearCiting document

Recent citations received in 2022
YearCiting document
2022Dryland vegetation pattern dynamics driven by inertial effects and secondary seed dispersal. (2022). Valenti, Giovanna ; Consolo, Giancarlo ; Grifo, Gabriele. In: Ecological Modelling. RePEc:eee:ecomod:v:474:y:2022:i:c:s0304380022002721.

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2022An Extended Thermodynamics Model for Blood Flow. (2022). Barbera, Elvira ; Pollino, Annamaria. In: Mathematics. RePEc:gam:jmathe:v:10:y:2022:i:16:p:2977-:d:891329.

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