Numerical Simulation of Thermo-Hydro-Mechanical Coupling of Model Test for Nuclear Waste Disposal by Yu-Ping Wang, Zhe Wang, Fa-Cheng Yi, Lei Fu, Ying Luo

“…Using the buffer material Mock-up test of multi-field coupling as a model, the partial differential equation (PDE) module in the general finite element software COMSOL Multiphysics was developed by a second development stage. …”
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A deep-learning approach to parameter fitting for a lithium metal battery cycling model, validated with experimental cell cycling time series by Maria Grazia Quarta, Ivonne Sgura, Elisa Emanuele, Jacopo Strada, Raquel Barreira, Benedetto Bozzini

“…This study contributes to shedding light on this highly technologically relevant problem, thanks to the combination of quantitative data exploitation and Partial Differential Equation (PDE) modelling for metal anode cycling. …”
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New exact soliton wave solutions appear in optical fibers with Sardar sub equation and new auxiliary equation techniques by Umair Asghar, Muhammad Imran Asjad, Yasser Salah Hamed, Ali Akgul, Murad Khan Hassani

“…These methods are applied to derive a wide range of soliton solutions for nonlinear partial differential equations. By transforming the original partial differential equation into an ordinary differential equation using an appropriate transformation, various types of solitary wave solutions are obtained. …”
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Partial Volume Reduction by Interpolation with Reverse Diffusion

“…The gray level of each subvoxel is considered as “material” able to move between subvoxels but not between voxels. A partial differential equation is written to allow the material to flow towards the highest gradient direction, creating a “reverse” diffusion process. …”
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Nonlinear compressive reduced basis approximation for PDE’s by Cohen, Albert, Farhat, Charbel, Maday, Yvon, Somacal, Agustin

“…Linear model reduction techniques design offline low-dimensional subspaces that are tailored to the approximation of solutions to a parameterized partial differential equation, for the purpose of fast online numerical simulations. …”
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Estimating the Force of Infection with Helicobacter pylori in Japan by Taishi Kayano, Ki-Deok Lee, Hiroshi Nishiura

“…Solving the McKendrick partial differential equation model, the seroprevalence was modeled as a function of survey year and age. …”
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Propagation of Shear Horizontal Wave at Magneto-Electro-Elastic Structure Subjected to Mechanically Imperfect Interface by Anandakrishnan Akshaya, Santosh Kumar, Kulandhaivel Hemalatha

“…This involves initially transforming the partial differential equation into an ordinary differential equation through basic variable separation and the ordinary differential equation is solved by WKB approximation technique. …”
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Weighted and Well-Balanced Nonlinear TV-Based Time-Dependent Model for Image Denoising by Khursheed Alam, Alka Chauhan, Santosh Kumar

“…The partial differential equation (PDE)-based models are widely used to remove additive Gaussian white noise and preserve edges, and one of the most widely used methods is the total variation denoising algorithm. …”
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The significance of heat transfer through natural convection in stagnation point flow of prandtl fluid by Salman Zeb, Zakir Ullah, A.B. Albidah, Ilyas Khan, Waqar A. Khan

“…The analysis integrates velocity, concentration slips, and temperature jumps within a nonlinear partial differential equation framework. These equations are converted into nonlinear partial differential equations using appropriate dimensionless variables. …”
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A Coupled Thermo-Hydromechanical Model of Soil Slope in Seasonally Frozen Regions under Freeze-Thaw Action by Yongxiang Zhan, Zheng Lu, Hailin Yao, Shaohua Xian

“…Based on the partial differential equation defined using the COMSOL Multiphysics software, a thermo-hydromechanical coupling model considering water migration, ice-water phase change, ice impedance, and frost heave is constructed, and the variations in the temperature field, migration of liquid water, accumulation of solid ice, and deformation of frost heave in frozen soil slopes are analysed. …”
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Three-Dimensional Inversion of Borehole-Surface Resistivity Method Based on the Unstructured Finite Element by Zhi Wang, Sinan Fang

“…The forward simulation and calculation start from the partial differential equation and the boundary conditions of the total potential of the three-dimensional point current source field are satisfied. …”
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Application of Image Denoising Method Based on Two-Way Coupling Diffusion Equation in Public Security Forensics by Yiqun Wang, Changpeng He, Zhenjiang Li

“…By improving the second-order partial differential equation, a new diffusion function with better diffusion effect than the original model is constructed. …”
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Physics-Informed Neural Networks for Modal Wave Field Predictions in 3D Room Acoustics by Stefan Schoder

“…PINNs are appealing since they can efficiently integrate a partial differential equation and experimental data by minimizing a loss function. …”
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Fourier method in the space of φB - distributions by V. S. Mokeichev, A. M. Sidorov

“…This offers a new perspective on the theory of solvability of linear problems, which is important for solving partial differential equations, especially equations with deviating arguments. …”
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Existence and Uniqueness of Mild Solutions to Impulsive Nonlocal Cauchy Problems by Mohamed Hannabou, Khalid Hilal, Ahmed Kajouni

“…Some concrete applications to partial differential equations are considered. Some concrete applications to partial differential equations are considered.…”
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Higher Order Compact Finite Difference Schemes for Unsteady Boundary Layer Flow Problems by P. G. Dlamini, S. S. Motsa, M. Khumalo

“…This work extends its applications to nonlinear partial differential equations modelling unsteady boundary layer flows. …”
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Third-Order Approximate Solution of Chemical Reaction-Diffusion Brusselator System Using Optimal Homotopy Asymptotic Method by Salem Alkhalaf

“…It is observed that the method is easy to implement and quite valuable for handling nonlinear system of partial differential equations and yielding excellent results at minimum computational cost. …”
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Existence of Some Semilinear Nonlocal Functional Differential Equations of Neutral Type by Hsiang Liu, Cheng-Wen Liao, Chin-Tzong Pang

“…The obtained results will be applied to a class of functional partial differential equations with nonlocal conditions.…”
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Solutions of type rm for a class of singular equations by Abdullah Altin

“…We obtain all solutions of radial type for a class of singular partial differential equations of even order. The essential operators here are elliptic or ultrahyperbolic.…”
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Nonlinear differential equations and algebraic systems by Lloyd K. Williams

“…The method is variation of parameters with asymptotic series and the theory of partial differential equations.…”
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