SN Partial Differential Equations and Applications Short Title: SN Partial Differ. Equ. Appl. Publisher: Springer Nature Switzerland, Basel ISSN: 2662-2963; 2662-2971/e Online: https://link.springer.com/journal/42985/volumes-and-issues Comments: Journal; Indexed cover-to-cover Documents Indexed: 264 Publications (since 2020) References Indexed: 258 Publications with 8,051 References. all top 5 Latest Issues 4, No. 6 (2023) 4, No. 5 (2023) 4, No. 4 (2023) 4, No. 3 (2023) 4, No. 2 (2023) 4, No. 1 (2023) 3, No. 6 (2022) 3, No. 5 (2022) 3, No. 4 (2022) 3, No. 3 (2022) 3, No. 2 (2022) 3, No. 1 (2022) 2, No. 6 (2021) 2, No. 5 (2021) 2, No. 4 (2021) 2, No. 3 (2021) 2, No. 2 (2021) 2, No. 1 (2021) 1, No. 6 (2020) 1, No. 5 (2020) 1, No. 4 (2020) 1, No. 3 (2020) 1, No. 2 (2020) 1, No. 1 (2020) all top 5 Authors 4 Ozawa, Tohru 3 Hayashi, Nakao 3 Jentzen, Arnulf 3 Melenk, Jens Markus 3 Shimizu, Senjo 3 Zhang, Zhitao 2 Alves, Claudianor Oliveira 2 Bartsch, Thomas J. 2 Bretti, Gabriella 2 Choulli, Mourad 2 Coclite, Giuseppe Maria 2 Da Silva, Edcarlos Domingos 2 Dalcín, Lisandro D. 2 Du, Yihong 2 Espath, Luis F. R. 2 Figueiredo, Giovany Malcher 2 Gala, Sadek 2 Giga, Yoshikazu 2 Gosse, Laurent 2 Grunert, Katrin 2 Hamamuki, Nao 2 Hutzenthaler, Martin 2 Ishige, Kazuhiro 2 Kaltenbacher, Manfred 2 Kruse, Thomas 2 Liu, Zhaoli 2 Mandel, Rainer 2 Naumkin, Pavel Ivanovich 2 Ogawa, Takayoshi 2 Pan, Xingbin 2 Parsani, Matteo 2 Ragusa, Maria Alessandra 2 Reigstad, Audun 2 Rieder, Alexander 2 Sauer, Niko 2 Sayas, Francisco-Javier 2 Taniuchi, Yasushi 2 ten Thije Boonkkamp, Jan H. M. 2 Tsai, Tai-Peng 2 Warin, Xavier 2 Yu, Yuanyang 2 Zanella, Mattia 1 Abdellaoui, Mohammed Amin 1 Abels, Helmut 1 Abiko, Keisuke 1 Abta, Abdelhadi 1 Alaa, Noureddine 1 Alejo, Miguel A. 1 Alexopoulos, Konstantinos 1 Almushaira, Mustafa 1 Aloui, Faouzia 1 Amaral, Sabrina 1 Amorim, Paulo 1 Andersson, Adam 1 Anthonissen, Martijn Johannes Hermanus 1 Apalara, Tijani Abdulaziz 1 Aqel, Fatima Al-Zahra’ 1 Araújo, Geraldo M. 1 Araujo, Marcos A. F. 1 Arima, Takashi 1 Arora, Rajan 1 Asai, Taisei 1 Attar, Kamel 1 Aurazo-Alvarez, Leithold L. 1 Bae, Hantaek 1 Bågmark, Kasper 1 Baldassari, Lorenzo 1 Barles, Guy 1 Başakoğlu, Engin 1 Beck, Geoffrey M. 1 Bell, Jonathan 1 Bellassoued, Mourad 1 Bellingeri, Carlo 1 Benhassine, Abderrazek 1 Berselli, Luigi Carlo 1 Bertens, Maikel W. M. C. 1 Bez, Neal 1 Bezerra, Flank David Morais 1 Bhattacharya, Debdeep 1 Bin-Saad, Maged Gumaan 1 Bo, Xiaomeng 1 Bobkov, Vladimir E. 1 Bögelein, Verena 1 Bokanowski, Olivier 1 Bölcskei, Helmut 1 Borachok, Ihor 1 Bottazzi, Emanuele 1 Boudjeriou, Tahir 1 Boutayeb, Salahaddine 1 Buchholz, Simone 1 Bueno, Hamilton P. 1 Caligaris, Carlo 1 Cardoso, Eleomar jun. 1 Carpenter, Mark H. 1 Carreño-Bolaños, Rafael 1 Carrião, Paulo Cesar 1 Carrisi, Maria Cristina 1 Carvajal, Xavier Paredes 1 Castillo, Ricardo 1 Castro, Javier Gutiérrez ...and 392 more Authors all top 5 Fields 218 Partial differential equations (35-XX) 49 Numerical analysis (65-XX) 37 Fluid mechanics (76-XX) 21 Operator theory (47-XX) 16 Probability theory and stochastic processes (60-XX) 14 Ordinary differential equations (34-XX) 13 Functional analysis (46-XX) 13 Differential geometry (53-XX) 12 Biology and other natural sciences (92-XX) 10 Global analysis, analysis on manifolds (58-XX) 10 Optics, electromagnetic theory (78-XX) 9 Dynamical systems and ergodic theory (37-XX) 9 Computer science (68-XX) 8 Real functions (26-XX) 8 Calculus of variations and optimal control; optimization (49-XX) 8 Statistical mechanics, structure of matter (82-XX) 6 Integral equations (45-XX) 6 Mechanics of deformable solids (74-XX) 6 Systems theory; control (93-XX) 5 Classical thermodynamics, heat transfer (80-XX) 4 General and overarching topics; collections (00-XX) 4 Mechanics of particles and systems (70-XX) 3 History and biography (01-XX) 3 Topological groups, Lie groups (22-XX) 3 Potential theory (31-XX) 3 Approximations and expansions (41-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Special functions (33-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Geophysics (86-XX) 1 Functions of a complex variable (30-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Integral transforms, operational calculus (44-XX) 1 Manifolds and cell complexes (57-XX) 1 Statistics (62-XX) 1 Quantum theory (81-XX) 1 Operations research, mathematical programming (90-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 128 Publications have been cited 425 times in 377 Documents Cited by ▼ Year ▼ A proof that rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear heat equations. Zbl 1455.65200 Hutzenthaler, Martin; Jentzen, Arnulf; Kruse, Thomas; Nguyen, Tuan Anh 56 2020 Neural networks-based backward scheme for fully nonlinear PDEs. Zbl 07341723 Pham, Huyên; Warin, Xavier; Germain, Maximilien 32 2021 Normalized solutions for a class of nonlinear Choquard equations. Zbl 1459.35173 Bartsch, Thomas; Liu, Yanyan; Liu, Zhaoli 23 2020 Multilevel Picard iterations for solving smooth semilinear parabolic heat equations. Zbl 1476.65273 E, Weinan; Hutzenthaler, Martin; Jentzen, Arnulf; Kruse, Thomas 21 2021 Solving high-dimensional Hamilton-Jacobi-Bellman PDEs using neural networks: perspectives from the theory of controlled diffusions and measures on path space. Zbl 1480.35101 Nüsken, Nikolas; Richter, Lorenz 19 2021 Entropy stable \(h/p\)-nonconforming discretization with the summation-by-parts property for the compressible Euler and Navier-Stokes equations. Zbl 1454.65123 Del Rey Fernández, David C.; Carpenter, Mark H.; Dalcin, Lisandro; Zampini, Stefano; Parsani, Matteo 11 2020 Deep neural network approximations for solutions of PDEs based on Monte Carlo algorithms. Zbl 1490.65232 Grohs, Philipp; Jentzen, Arnulf; Salimova, Diyora 11 2022 Numerical continuation for a fast-reaction system and its cross-diffusion limit. Zbl 1451.35237 Kuehn, Christian; Soresina, Cinzia 9 2020 (Non)-convergence of solutions of the convective Allen-Cahn equation. Zbl 1513.76158 Abels, Helmut 6 2022 Partial regularity of weak solutions and life-span of smooth solutions to a biological network formulation model. Zbl 1456.35062 Xu, Xiangsheng 6 2020 Dynamic boundary conditions and the Carslaw-Jaeger constitutive relation in heat transfer. Zbl 1457.35014 Sauer, Niko 6 2020 Multi-domain spectral approach for the Hilbert transform on the real line. Zbl 1490.44005 Klein, Christian; Riton, Julien; Stoilov, Nikola 5 2021 Improved regularity criterion for the 3D Navier-Stokes equations via the gradient of one velocity component. Zbl 1476.35172 Gala, Sadek; Ragusa, Maria Alessandra 5 2021 Modal approximation for plasmonic resonators in the time domain: the scalar case. Zbl 1507.35268 Baldassari, Lorenzo; Millien, Pierre; Vanel, Alice L. 5 2021 Lower bound estimate for the dissipative nonlinear Schrödinger equation. Zbl 1476.35249 Sato, Takuya 5 2021 Transport and continuity equations with (very) rough noise. Zbl 1479.35966 Bellingeri, C.; Djurdjevac, A.; Friz, P. K.; Tapia, N. 4 2021 Global well-posedness for the fractional Boussinesq-Coriolis system with stratification in a framework of Fourier-Besov type. Zbl 1484.76083 Aurazo-Alvarez, Leithold L.; Ferreira, Lucas C. F. 4 2021 On vanishing and localizing around corners of electromagnetic transmission resonances. Zbl 1477.78003 Diao, Huaian; Liu, Hongyu; Wang, Xianchao; Yang, Ke 4 2021 Decay in the one dimensional generalized improved Boussinesq equation. Zbl 1451.35133 Maulén, Christopher; Muñoz, Claudio 4 2020 Long time behavior of a model for the evolution of morphogens in a growing tissue. Zbl 1454.35032 Coclite, G. M.; Coclite, M. M. 4 2020 Viscosity solutions for the crystalline mean curvature flow with a nonuniform driving force term. Zbl 1456.35080 Giga, Yoshikazu; Požár, Norbert 4 2020 Fourth-order time-stepping compact finite difference method for multi-dimensional space-fractional coupled nonlinear Schrödinger equations. Zbl 1460.35306 Almushaira, Mustafa; Liu, Fei 4 2020 Local existence and nonexistence for fractional in time weakly coupled reaction-diffusion systems. Zbl 1460.35379 Suzuki, Masamitsu 4 2021 A game-theoretic approach to dynamic boundary problems for level-set curvature flow equations and applications. Zbl 1479.35226 Hamamuki, Nao; Liu, Qing 3 2021 Attraction-repulsion taxis mechanisms in a predator-prey model. Zbl 1479.35070 Bell, Jonathan; Haskell, Evan C. 3 2021 Equivalences of PDE systems associated to degenerate para-CR structures: foundational aspects. Zbl 1479.35038 Merker, Joël 3 2022 Hardy type inequalities with spherical derivatives. Zbl 1451.26021 Bez, Neal; Machihara, Shuji; Ozawa, Tohru 3 2020 Remarks on optimal rates of convergence in periodic homogenization of linear elliptic equations in non-divergence form. Zbl 1459.35022 Guo, Xiaoqin; Tran, Hung V.; Yu, Yifeng 3 2020 Fast hybrid numerical-asymptotic boundary element methods for high frequency screen and aperture problems based on least-squares collocation. Zbl 1452.65381 Gibbs, A.; Hewett, D. P.; Huybrechs, D.; Parolin, E. 3 2020 Finer analysis of the Nehari set associated to a class of Kirchhoff-type equations. Zbl 1458.35190 Silva, Kaye; Sousa, Steffânio M. 3 2020 Liouville theorems for parabolic systems with homogeneous nonlinearities and gradient structure. Zbl 1487.35142 Quittner, Pavol 3 2022 Dynamical universality for random matrices. Zbl 1486.60015 Kawamoto, Yosuke; Osada, Hirofumi 3 2022 A remake of Bourgain-Brezis-Mironescu characterization of Sobolev spaces. Zbl 07703078 Foghem Gounoue, Guy Fabrice 3 2023 Helmholtz’s decomposition for compressible flows and its application to computational aeroacoustics. Zbl 1457.76016 Schoder, Stefan; Roppert, Klaus; Kaltenbacher, Manfred 3 2020 Concentration, existence of a ground state and multiplicity of solutions for a subcritical elliptic system via penalization method. Zbl 1465.35175 Figueiredo, Giovany M.; Salirrosas, Segundo Manuel A. 3 2021 Regularity of the \(m\)-symphonic map. Zbl 1464.58005 Misawa, Masashi; Nakauchi, Nobumitsu 3 2021 Large time asymptotics for the fractional modified Korteweg-de Vries equation with \(\alpha \in \left(2,4\right)\). Zbl 1501.35059 Hayashi, Nakao; Naumkin, Pavel I.; Sánchez-Suárez, Isahi 3 2022 Weak-strong uniqueness for the isentropic Euler equations with possible vacuum. Zbl 1496.35299 Ghoshal, Shyam Sundar; Jana, Animesh; Wiedemann, Emil 3 2022 Blow up of solutions of semilinear wave equations related to nonlinear waves in de Sitter spacetime. Zbl 1479.35864 Tsutaya, Kimitoshi; Wakasugi, Yuta 3 2022 Sobolev estimates for non-uniformly parabolic PDEs. Zbl 1484.35097 Schochet, Steve 3 2022 The Keller-Segel system on bounded convex domains in critical spaces. Zbl 1476.35287 Hieber, Matthias; Kress, Klaus; Stinner, Christian 2 2021 Remarks on the generalized Cauchy-Dirichlet problem for graph mean curvature flow with driving force. Zbl 1479.35111 Mitake, Hiroyoshi; Zhang, Longjie 2 2021 Existence and concentration of solution for Schrödinger-Poisson system with local potential. Zbl 1479.35055 Yang, Zhipeng; Yu, Yuanyang 2 2021 High-dimensional distribution generation through deep neural networks. Zbl 1523.65017 Perekrestenko, Dmytro; Eberhard, Léandre; Bölcskei, Helmut 2 2021 Development and analysis of entropy stable no-slip wall boundary conditions for the Eulerian model for viscous and heat conducting compressible flows. Zbl 1477.65169 Sayyari, Mohammed; Dalcin, Lisandro; Parsani, Matteo 2 2021 On some regularity results of parabolic problems with nonlinear perturbed terms and general data. Zbl 1479.35155 Abdellaoui, M.; Redwane, H. 2 2022 Maximal regularity and a singular limit problem for the Patlak-Keller-Segel system in the scaling critical space involving BMO. Zbl 1487.35037 Kurokiba, Masaki; Ogawa, Takayoshi 2 2022 Existence of positive solutions to Kirchhoff equations with vanishing potentials and general nonlinearity. Zbl 1455.35093 Sun, Dongdong; Zhang, Zhitao 2 2020 Asymptotic behavior for a class of derivative nonlinear Schrödinger systems. Zbl 1451.35187 Katayama, Soichiro; Sakoda, Daisuke 2 2020 Stability analysis of a delayed SIR epidemic model with diffusion and saturated incidence rate. Zbl 1454.35391 Abta, Abdelhadi; Boutayeb, Salahaddine; Laarabi, Hassan; Rachik, Mostafa; Alaoui, Hamad Talibi 2 2020 A game theoretical approach for a nonlinear system driven by elliptic operators. Zbl 1455.35081 Miranda, Alfredo; Rossi, Julio D. 2 2020 Structure aware Runge-Kutta time stepping for spacetime tents. Zbl 1452.65232 Gopalakrishnan, Jay; Schöberl, Joachim; Wintersteiger, Christoph 2 2020 A discontinuous Galerkin Trefftz type method for solving the two dimensional Maxwell equations. Zbl 1452.76088 Fure, Håkon Sem; Pernet, Sébastien; Sirdey, Margot; Tordeux, Sébastien 2 2020 Partial symmetry of normalized solutions for a doubly coupled Schrödinger system. Zbl 1456.35008 Luo, Haijun; Zhang, Zhitao 2 2020 Strictly convex solutions for singular Monge-Ampère equations with nonlinear gradient terms: existence and boundary asymptotic behavior. Zbl 1455.35128 Feng, Meiqiang; Sun, Huayuan; Zhang, Xuemei 2 2020 Minimal submanifolds in a metric measure space. Zbl 1456.53050 Cheng, Xu; Zhou, Detang 2 2020 Nontrivial solutions to non-local problems with sublinear or superlinear nonlinearities. Zbl 1458.35452 Han, Zhiqing; Xue, Ye 2 2020 Finite time blow-up for a nonlinear viscoelastic Petrovsky equation with high initial energy. Zbl 1460.35232 Liu, Lishan; Sun, Fenglong; Wu, Yonghong 2 2020 The Brezis-Nirenberg type double critical problem for the Choquard equation. Zbl 1458.35196 Cai, Li; Zhang, Fubao 2 2020 Propagation, diffusion and free boundaries. Zbl 1465.35004 Du, Yihong 2 2020 Calderón-Zygmund theory for non-convolution type nonlocal equations with continuous coefficient. Zbl 1487.35133 Fall, Mouhamed Moustapha; Mengesha, Tadele; Schikorra, Armin; Yeepo, Sasikarn 2 2022 Existence of a minimizer for a nonlinear Schrödinger system with three wave interaction under non-symmetric potentials. Zbl 1484.35348 Osada, Yuki 2 2022 Applications of \(p\)-harmonic transplantation for functional inequalities involving a Finsler norm. Zbl 1484.26027 Habibi, Sadaf; Takahashi, Futoshi 2 2022 Multilane analysis of a viscous second-order macroscopic traffic flow model. Zbl 1465.35303 Fosu, Gabriel Obed; Tabi Oduro, Francis; Caligaris, Carlo 2 2021 Liouville type theorems for stationary Navier-Stokes equations. Zbl 1462.35113 Tsai, Tai-Peng 2 2021 Precise blowup rate near the boundary of boundary blowup solutions to \(k\)-Hessian equation. Zbl 1465.35265 Takimoto, Kazuhiro 2 2021 On averaged exponential integrators for semilinear wave equations with solutions of low-regularity. Zbl 1460.65055 Buchholz, Simone; Dörich, Benjamin; Hochbruck, Marlis 2 2021 On well-posedness of the Cauchy problem for 3D MHD system in critical Sobolev-Gevrey space. Zbl 1464.35212 Chaabani, Abdelkerim 2 2021 On the Hölder regularity for solutions of integro-differential equations like the anisotropic fractional Laplacian. Zbl 1462.35115 dos Santos, E. B.; Leitão, R. 2 2021 Uniform estimates for fractional operators. Zbl 1464.35176 Farwig, Reinhard; Tsuda, Kazuyuki 2 2021 Exhaustive existence and non-existence results for Hardy-Hénon equations in \(\mathbb{R}^n\). Zbl 1504.35102 Giga, Yoshikazu; Ngô, Quốc Anh 2 2022 Eckhaus instability of stationary patterns in hyperbolic reaction-diffusion models on large finite domains. Zbl 1498.35033 Consolo, Giancarlo; Grifó, Gabriele 2 2022 Newton’s second law with a semiconvex potential. Zbl 1490.35272 Hynd, Ryan 2 2022 Asymptotic analysis of subwavelength halide perovskite resonators. Zbl 1504.35515 Alexopoulos, Konstantinos; Davies, Bryn 2 2022 On the existence of positive solutions to a certain class of semilinear elliptic equations. Zbl 1480.35262 Ikoma, Norihisa 1 2021 Diffusive limit of a two-dimensional well-balanced approximation to a kinetic model of chemotaxis. Zbl 1480.92033 Bretti, Gabriella; Gosse, Laurent 1 2021 An alternative proof of \(L^q-L^r\) estimates of the Oseen semigroup in higher dimensional exterior domains. Zbl 1491.76022 Hishida, Toshiaki 1 2021 On the spectral stability of periodic traveling waves for the critical Korteweg-de Vries and Gardner equations. Zbl 1490.76051 Natali, Fábio; Cardoso, Eleomar; Amaral, Sabrina 1 2021 On sublinear fractional Schrödinger-Poisson systems. Zbl 1479.49014 Benhassine, Abderrazek 1 2021 Minimal brake orbits of first-order convex Hamiltonian systems with anisotropic growth. Zbl 1476.34104 Zhang, Xiaofei; Liu, Chungen 1 2021 Regularity properties of the cubic biharmonic Schrödinger equation on the half line. Zbl 1483.35197 Başakoğlu, Engin 1 2021 Scattering resonances for a three-dimensional subwavelength hole. Zbl 1480.35097 Fatima, Maryam; Lin, Junshan 1 2021 Scattering for quadratic-type Schrödinger systems in dimension five without mass-resonance. Zbl 1476.35246 Noguera, Norman; Pastor, Ademir 1 2021 Traveling waves for the nonlinear variational wave equation. Zbl 1480.35087 Grunert, Katrin; Reigstad, Audun 1 2021 The unique continuation property for second order evolution PDEs. Zbl 1480.35080 Choulli, Mourad 1 2021 Inhomogeneous Dirichlet boundary value problem for nonlinear Schrödinger equations in the upper half-space. Zbl 1476.35198 Hayashi, Nakao; Kaikina, Elena I.; Ogawa, Takayoshi 1 2021 Local gradient estimates for second-order nonlinear elliptic and parabolic equations by the weak Bernstein’s method. Zbl 1480.35069 Barles, G. 1 2021 Evolving to non-round Weingarten spheres: integer linear Hopf flows. Zbl 1480.35276 Guilfoyle, Brendan; Klingenberg, Wilhelm 1 2021 A note on 2D Navier-Stokes equations. Zbl 1476.35170 Fan, Jishan; Ozawa, Tohru 1 2021 On the rate of error growth in time for numerical solutions of nonlinear dispersive wave equations. Zbl 1476.65271 Ranocha, Hendrik; de Luna, Manuel Quezada; Ketcheson, David I. 1 2021 One-dimensional symmetry of positive bounded solutions to the nonlinear Schrödinger equation in the half-space in two and three dimensions. Zbl 1479.35041 Sourdis, Christos 1 2021 Characterization of harmonic functions by the behavior of means at a single point. Zbl 1460.31009 Estrada, Ricardo 1 2020 The exterior Calderón operator for non-spherical objects. Zbl 1455.35253 Kristensson, Gerhard; Stratis, Ioannis G.; Wellander, Niklas; Yannacopoulos, Athanasios N. 1 2020 The topological contribution of the critical points at infinity for critical fractional Yamabe-type equations. Zbl 1458.35161 Abdullah Sharaf, Khadijah; Chtioui, Hichem 1 2020 ABP maximum principles for fully nonlinear integro-differential equations with unbounded inhomogeneous terms. Zbl 1458.35087 Kitano, Shuhei 1 2020 Sweeping preconditioners for stratified media in the presence of reflections. Zbl 1455.65044 Preuß, Janosch; Hohage, Thorsten; Lehrenfeld, Christoph 1 2020 Positive and negative solutions for the nonlinear fractional Kirchhoff equation in \(\mathbb{R}^N \). Zbl 1455.35094 Wang, Yang; Liu, Yansheng 1 2020 Nodal bubble tower solutions to slightly subcritical elliptic problems with Hardy terms. Zbl 1455.35027 Bartsch, Thomas; Guo, Qianqiao 1 2020 On spectral asymptotics and bifurcation for carrier equations with odd superlinear term. Zbl 1455.35097 Zhang, Yu; Yan, Baoqiang 1 2020 All the generalized characteristics for the solution to a Hamilton-Jacobi equation with the initial data of the Takagi function. Zbl 1456.35082 Fujita, Yasuhiro; Hamamuki, Nao; Yamaguchi, Norikazu 1 2020 A remake of Bourgain-Brezis-Mironescu characterization of Sobolev spaces. Zbl 07703078 Foghem Gounoue, Guy Fabrice 3 2023 General decay of the solution to a nonlinear viscoelastic beam with delay. Zbl 1518.35106 Khemmoudj, Ammar 1 2023 Global logarithmic stability of a Cauchy problem for anisotropic wave equations. Zbl 1518.35171 Bellassoued, Mourad; Choulli, Mourad 1 2023 On an indefinite nonhomogeneous equation with critical exponential growth. Zbl 1520.35077 Sousa, Karla Carolina V. de; Tavares, Leandro S. 1 2023 Fourth-order nonlinear degenerate problem for image decomposition. Zbl 1521.35212 Nokrane, Ahmed; Alaa, Nour Eddine; Aqel, Fatima 1 2023 Higher-order error estimates for physics-informed neural networks approximating the primitive equations. Zbl 07726379 Hu, Ruimeng; Lin, Quyuan; Raydan, Alan; Tang, Sui 1 2023 A continuum framework for phase field with bulk-surface dynamics. Zbl 1513.74138 Espath, Luis 1 2023 Deep neural network approximations for solutions of PDEs based on Monte Carlo algorithms. Zbl 1490.65232 Grohs, Philipp; Jentzen, Arnulf; Salimova, Diyora 11 2022 (Non)-convergence of solutions of the convective Allen-Cahn equation. Zbl 1513.76158 Abels, Helmut 6 2022 Equivalences of PDE systems associated to degenerate para-CR structures: foundational aspects. Zbl 1479.35038 Merker, Joël 3 2022 Liouville theorems for parabolic systems with homogeneous nonlinearities and gradient structure. Zbl 1487.35142 Quittner, Pavol 3 2022 Dynamical universality for random matrices. Zbl 1486.60015 Kawamoto, Yosuke; Osada, Hirofumi 3 2022 Large time asymptotics for the fractional modified Korteweg-de Vries equation with \(\alpha \in \left(2,4\right)\). Zbl 1501.35059 Hayashi, Nakao; Naumkin, Pavel I.; Sánchez-Suárez, Isahi 3 2022 Weak-strong uniqueness for the isentropic Euler equations with possible vacuum. Zbl 1496.35299 Ghoshal, Shyam Sundar; Jana, Animesh; Wiedemann, Emil 3 2022 Blow up of solutions of semilinear wave equations related to nonlinear waves in de Sitter spacetime. Zbl 1479.35864 Tsutaya, Kimitoshi; Wakasugi, Yuta 3 2022 Sobolev estimates for non-uniformly parabolic PDEs. Zbl 1484.35097 Schochet, Steve 3 2022 On some regularity results of parabolic problems with nonlinear perturbed terms and general data. Zbl 1479.35155 Abdellaoui, M.; Redwane, H. 2 2022 Maximal regularity and a singular limit problem for the Patlak-Keller-Segel system in the scaling critical space involving BMO. Zbl 1487.35037 Kurokiba, Masaki; Ogawa, Takayoshi 2 2022 Calderón-Zygmund theory for non-convolution type nonlocal equations with continuous coefficient. Zbl 1487.35133 Fall, Mouhamed Moustapha; Mengesha, Tadele; Schikorra, Armin; Yeepo, Sasikarn 2 2022 Existence of a minimizer for a nonlinear Schrödinger system with three wave interaction under non-symmetric potentials. Zbl 1484.35348 Osada, Yuki 2 2022 Applications of \(p\)-harmonic transplantation for functional inequalities involving a Finsler norm. Zbl 1484.26027 Habibi, Sadaf; Takahashi, Futoshi 2 2022 Exhaustive existence and non-existence results for Hardy-Hénon equations in \(\mathbb{R}^n\). Zbl 1504.35102 Giga, Yoshikazu; Ngô, Quốc Anh 2 2022 Eckhaus instability of stationary patterns in hyperbolic reaction-diffusion models on large finite domains. Zbl 1498.35033 Consolo, Giancarlo; Grifó, Gabriele 2 2022 Newton’s second law with a semiconvex potential. Zbl 1490.35272 Hynd, Ryan 2 2022 Asymptotic analysis of subwavelength halide perovskite resonators. Zbl 1504.35515 Alexopoulos, Konstantinos; Davies, Bryn 2 2022 Ground states for Maxwell’s equations in nonlocal nonlinear media. Zbl 1489.35089 Mandel, Rainer 1 2022 Global in time solvability for a semilinear heat equation without the self-similar structure. Zbl 1487.35116 Fujishima, Yohei; Ioku, Norisuke 1 2022 Transport equations with inflow boundary conditions. Zbl 1491.35386 Scott, L. Ridgway; Pollock, Sara 1 2022 Cauchy problem for the ES-BGK model with the correct Prandtl number. Zbl 1486.82035 Son, Sung-jun; Yun, Seok-Bae 1 2022 A new nonlocal calculus framework. Helmholtz decompositions, properties, and convergence for nonlocal operators in the limit of the vanishing horizon. Zbl 07532101 Haar, Andrew; Radu, Petronela 1 2022 Deep learning schemes for parabolic nonlocal integro-differential equations. Zbl 1515.60249 Castro, Javier 1 2022 On the initial-boundary value problem for a non-local elliptic-hyperbolic system related to the short pulse equation. Zbl 1504.35141 Coclite, Giuseppe Maria; di Ruvo, Lorenzo 1 2022 Rectifiability of divergence-free fields along invariant 2-tori. Zbl 1492.76151 Perrella, David; Pfefferlé, David; Stoyanov, Luchezar 1 2022 Monte Carlo stochastic Galerkin methods for non-Maxwellian kinetic models of multiagent systems with uncertainties. Zbl 1492.82025 Medaglia, Andrea; Tosin, Andrea; Zanella, Mattia 1 2022 Local regularity conditions on initial data for local energy solutions of the Navier-Stokes equations. Zbl 1480.35311 Kang, Kyungkeun; Miura, Hideyuki; Tsai, Tai-Peng 1 2022 Space-time analytic smoothing effect for the cubic nonlinear Schrödinger equations without pseudo-conformal invariance. Zbl 1480.35353 Hoshino, Gaku 1 2022 A method of fundamental solutions with time-discretisation for wave motion from lateral Cauchy data. Zbl 1490.65183 Borachok, Ihor; Chapko, Roman; Johansson, B. Tomas 1 2022 Neural networks-based backward scheme for fully nonlinear PDEs. Zbl 07341723 Pham, Huyên; Warin, Xavier; Germain, Maximilien 32 2021 Multilevel Picard iterations for solving smooth semilinear parabolic heat equations. Zbl 1476.65273 E, Weinan; Hutzenthaler, Martin; Jentzen, Arnulf; Kruse, Thomas 21 2021 Solving high-dimensional Hamilton-Jacobi-Bellman PDEs using neural networks: perspectives from the theory of controlled diffusions and measures on path space. Zbl 1480.35101 Nüsken, Nikolas; Richter, Lorenz 19 2021 Multi-domain spectral approach for the Hilbert transform on the real line. Zbl 1490.44005 Klein, Christian; Riton, Julien; Stoilov, Nikola 5 2021 Improved regularity criterion for the 3D Navier-Stokes equations via the gradient of one velocity component. Zbl 1476.35172 Gala, Sadek; Ragusa, Maria Alessandra 5 2021 Modal approximation for plasmonic resonators in the time domain: the scalar case. Zbl 1507.35268 Baldassari, Lorenzo; Millien, Pierre; Vanel, Alice L. 5 2021 Lower bound estimate for the dissipative nonlinear Schrödinger equation. Zbl 1476.35249 Sato, Takuya 5 2021 Transport and continuity equations with (very) rough noise. Zbl 1479.35966 Bellingeri, C.; Djurdjevac, A.; Friz, P. K.; Tapia, N. 4 2021 Global well-posedness for the fractional Boussinesq-Coriolis system with stratification in a framework of Fourier-Besov type. Zbl 1484.76083 Aurazo-Alvarez, Leithold L.; Ferreira, Lucas C. F. 4 2021 On vanishing and localizing around corners of electromagnetic transmission resonances. Zbl 1477.78003 Diao, Huaian; Liu, Hongyu; Wang, Xianchao; Yang, Ke 4 2021 Local existence and nonexistence for fractional in time weakly coupled reaction-diffusion systems. Zbl 1460.35379 Suzuki, Masamitsu 4 2021 A game-theoretic approach to dynamic boundary problems for level-set curvature flow equations and applications. Zbl 1479.35226 Hamamuki, Nao; Liu, Qing 3 2021 Attraction-repulsion taxis mechanisms in a predator-prey model. Zbl 1479.35070 Bell, Jonathan; Haskell, Evan C. 3 2021 Concentration, existence of a ground state and multiplicity of solutions for a subcritical elliptic system via penalization method. Zbl 1465.35175 Figueiredo, Giovany M.; Salirrosas, Segundo Manuel A. 3 2021 Regularity of the \(m\)-symphonic map. Zbl 1464.58005 Misawa, Masashi; Nakauchi, Nobumitsu 3 2021 The Keller-Segel system on bounded convex domains in critical spaces. Zbl 1476.35287 Hieber, Matthias; Kress, Klaus; Stinner, Christian 2 2021 Remarks on the generalized Cauchy-Dirichlet problem for graph mean curvature flow with driving force. Zbl 1479.35111 Mitake, Hiroyoshi; Zhang, Longjie 2 2021 Existence and concentration of solution for Schrödinger-Poisson system with local potential. Zbl 1479.35055 Yang, Zhipeng; Yu, Yuanyang 2 2021 High-dimensional distribution generation through deep neural networks. 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P.; Huybrechs, D.; Parolin, E. 3 2020 ...and 28 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 723 Authors 18 Jentzen, Arnulf 10 Hutzenthaler, Martin 7 Grohs, Philipp 6 Kruse, Thomas 6 Maniar, Lahcen 5 Dalcín, Lisandro D. 5 Liu, Hongyu 5 Parsani, Matteo 5 Schneider, Reinhold 4 Beck, Christian 4 Boukharfane, Radouan 4 Chorfi, Salah-Eddine 4 Cingolani, Silvia 4 Del Rey Fernández, David C. 4 Kühn, Christian 4 Nguwi, Jiang Yu 4 Privault, Nicolas 4 Sato, Takuya 4 Soresina, Cinzia 4 Warin, Xavier 4 Yang, Haizhao 3 Allalou, Chakir 3 Becker, Sebastian 3 Chan, Jesse 3 E, Weinan 3 El Guermai, Ghita 3 Figueiredo, Giovany Malcher 3 Germain, Maximilien 3 Giga, Yoshikazu 3 Hamamuki, Nao 3 Han, Jiequn 3 He, Xiaoming 3 Hornung, Fabian 3 Klein, Christian 3 Li, Bin 3 Li, Xinfu 3 Merker, Joël 3 Nakauchi, Nobumitsu 3 Naumkin, Pavel Ivanovich 3 Nguyen, Tuan-Anh 3 Nüsken, Nikolas 3 Osada, Hirofumi 3 Ozawa, Tohru 3 Petersen, Philipp Christian 3 Salirrosas, Segundo Manuel A. 3 Stoilov, Nikola M. 3 Svärd, Magnus 3 Tanaka, Kazunaga 3 von Wurstemberger, Philippe 3 Yamada, Toshihiro 3 Zhang, Zhitao 2 Almushaira, Mustafa 2 Azanzal, Achraf 2 Bell, Jonathan 2 Benth, Fred Espen 2 Byun, Sun-Sig 2 Carreño-Bolaños, Rafael 2 Chen, Jianqing 2 Chen, Zhewen 2 Cho, Youseung 2 Choulli, Mourad 2 Consolo, Giancarlo 2 Detering, Nils 2 Farwig, Reinhard 2 Galimberti, Luca 2 Gallo, Marco 2 Gopalakrishnan, Jay 2 Grifó, Gabriele 2 Gu, Yiqi 2 Guo, Zhao 2 Hartmann, Carsten 2 Haskell, Evan C. 2 Hayashi, Nakao 2 Huybrechs, Daan 2 Kalise, Dante 2 Ketcheson, David I. 2 Keyes, David Elliot 2 Khoutaibi, Abdelaziz 2 Kim, Minhyun 2 Kita, Naoyasu 2 Kuckuck, Benno 2 Kutyniok, Gitta 2 Li, Fuyi 2 Liu, Qing 2 Liu, Yikan 2 Long, Lei 2 Machihara, Shuji 2 Maierhofer, Georg 2 Maulén, Christopher 2 Melliani, Said 2 Meng, Yuxi 2 Millien, Pierre 2 Miranda, Alfredo C. 2 Nolasco, Irving Reyna 2 Nurowski, Paweł 2 Oster, Mathias 2 Oukdach, Omar 2 Palmieri, Alessandro 2 Penent, Guillaume 2 Pham, Huyên ...and 623 more Authors all top 5 Cited in 171 Journals 13 Journal of Mathematical Analysis and Applications 12 Journal of Computational Physics 12 The Journal of Geometric Analysis 10 Calculus of Variations and Partial Differential Equations 10 SN Partial Differential Equations and Applications 9 SIAM Journal on Scientific Computing 9 Discrete and Continuous Dynamical Systems 8 ZAMP. Zeitschrift für angewandte Mathematik und Physik 8 Journal of Scientific Computing 7 Journal of Differential Equations 6 Applied Mathematics and Computation 6 NoDEA. Nonlinear Differential Equations and Applications 5 Journal of Mathematical Physics 5 Mathematical Methods in the Applied Sciences 5 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 5 Advances in Computational Mathematics 5 Multiscale Modeling & Simulation 5 Discrete and Continuous Dynamical Systems. Series S 5 Journal of Elliptic and Parabolic Equations 4 Computers & Mathematics with Applications 4 Mathematics of Computation 4 SIAM Journal on Numerical Analysis 4 Studies in Applied Mathematics 4 Physica D 4 Applied Mathematics Letters 4 Journal de Mathématiques Pures et Appliquées. Neuvième Série 4 SIAM Journal on Mathematical Analysis 4 Nonlinear Analysis. Real World Applications 4 Discrete and Continuous Dynamical Systems. 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Second Series 2 Journal of Numerical Mathematics 2 Analysis and Applications (Singapore) 2 International Journal of Computational Methods 2 Acta Numerica 2 Oberwolfach Reports 2 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 2 Complex Variables and Elliptic Equations 2 Communications in Computational Physics 2 Journal of Pseudo-Differential Operators and Applications 2 Statistics and Computing 2 Evolution Equations and Control Theory 2 Journal of Computational Dynamics 2 Minimax Theory and its Applications 2 SIAM Journal on Mathematics of Data Science 1 Applicable Analysis 1 Archive for Rational Mechanics and Analysis 1 Bulletin of the Australian Mathematical Society 1 Computer Methods in Applied Mechanics and Engineering 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Journal of Statistical Physics 1 Letters in Mathematical Physics 1 Physica A 1 Ukrainian Mathematical Journal 1 Bulletin of Mathematical Biology 1 Chaos, Solitons and Fractals 1 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Applied Mathematics and Optimization 1 Archiv der Mathematik 1 Calcolo 1 Information Sciences 1 Integral Equations and Operator Theory 1 International Economic Review 1 International Journal for Numerical Methods in Engineering 1 Manuscripta Mathematica 1 Mathematische Nachrichten 1 Mathematische Zeitschrift 1 Meccanica 1 Memoirs of the American Mathematical Society 1 Proceedings of the American Mathematical Society 1 Quarterly of Applied Mathematics 1 SIAM Journal on Control and Optimization 1 Theoretical Population Biology 1 Bulletin of the Korean Mathematical Society 1 Asymptotic Analysis 1 Sugaku Expositions ...and 71 more Journals all top 5 Cited in 39 Fields 256 Partial differential equations (35-XX) 115 Numerical analysis (65-XX) 54 Computer science (68-XX) 47 Fluid mechanics (76-XX) 45 Probability theory and stochastic processes (60-XX) 24 Biology and other natural sciences (92-XX) 24 Systems theory; control (93-XX) 21 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 14 Differential geometry (53-XX) 13 Ordinary differential equations (34-XX) 13 Functional analysis (46-XX) 12 Calculus of variations and optimal control; optimization (49-XX) 11 Operator theory (47-XX) 10 Dynamical systems and ergodic theory (37-XX) 10 Global analysis, analysis on manifolds (58-XX) 10 Mechanics of deformable solids (74-XX) 10 Statistical mechanics, structure of matter (82-XX) 9 Real functions (26-XX) 9 Approximations and expansions (41-XX) 8 Harmonic analysis on Euclidean spaces (42-XX) 7 Optics, electromagnetic theory (78-XX) 6 Integral equations (45-XX) 6 Statistics (62-XX) 6 Quantum theory (81-XX) 5 Operations research, mathematical programming (90-XX) 4 Several complex variables and analytic spaces (32-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Potential theory (31-XX) 3 Special functions (33-XX) 3 Mechanics of particles and systems (70-XX) 2 General and overarching topics; collections (00-XX) 2 Measure and integration (28-XX) 2 Integral transforms, operational calculus (44-XX) 2 Classical thermodynamics, heat transfer (80-XX) 2 Geophysics (86-XX) 1 Number theory (11-XX) 1 Topological groups, Lie groups (22-XX) 1 Functions of a complex variable (30-XX) 1 Difference and functional equations (39-XX) Citations by Year