Similarity Solutions of Partial Differential Equations in Probability by Mario Lefebvre

“…The appropriate partial differential equations are solved explicitly by using the method of similarity solutions and the method of separation of variables. …”
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Solutions of Smooth Nonlinear Partial Differential Equations by Jan Harm van der Walt

“…The method of order completion provides a general and type-independent theory for the existence and basic regularity of the solutions of large classes of systems of nonlinear partial differential equations (PDEs). Recently, the application of convergence spaces to this theory resulted in a significant improvement upon the regularity of the solutions and provided new insight into the structure of solutions. …”
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On simplification system of partial differential equations with variable by Donatas Jurgaitis

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The Conical Radial Basis Function for Partial Differential Equations by J. Zhang, F. Z. Wang, E. R. Hou

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Recent development in the theory of linear partial differential equations by Jean Dieudonné

“…A historical development of the theory of linear partial differential equation is reviewed with comments. A recent development in the theory of linear partial differential equations is discussed.…”
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Advances in Nonlinear Complexity Analysis for Partial Differential Equations by Zhengde Dai, Qianshun S. Chang, Lan Xu, Syed Tauseef Mohyud-Din, Hafez Tari, Peicheng Zhu

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Analytical reduction of a system of partial differential equations by Donatas Jurgaitis

“… A system of four of the first order partial differential equations is transformed into the system, which has blocked diagonal matrix. …”
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Linear neutral partial differential equations: a semigroup approach by Rainer Nagel, Nguyen Thieu Huy

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On closed-form solutions of some nonlinear partial differential equations by S. S. Okoya

“…This paper is devoted to closed-form solutions of the partial differential equation: θxx+θyy+δexp(θ)=0, which arises in the steady state thermal explosion theory. …”
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A New Approach for Solving Fractional Partial Differential Equations by Fanwei Meng

“…This approach can be suitable for solving fractional partial differential equations with more general forms than the method proposed by S. …”
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Partial Differential Equations-Based Segmentation for Radiotherapy Treatment Planning by Frédéric Gibou, Doron Levy, Carlos Cárdenas, Pingyu Liu, Arthur Boyer

“…We develop new image processing techniques that are based on solving a partial differential equation for theevolution of the curve that identifies the segmented organ. …”
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Solving Nonlinear Partial Differential Equations by the sn-ns Method by Alvaro H. Salas

“…We present the application of the sn-ns method to solve nonlinear partial differential equations. We show that the well-known tanh-coth method is a particular case of the sn-ns method.…”
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Bilinear Equation of the Nonlinear Partial Differential Equation and Its Application by Xiao-Feng Yang, Yi Wei

“…The homogeneous balance of undetermined coefficient method is firstly proposed to derive a more general bilinear equation of the nonlinear partial differential equation (NLPDE). By applying perturbation method, subsidiary ordinary differential equation (sub-ODE) method, and compatible condition to bilinear equation, more exact solutions of NLPDE are obtained. …”
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A survey of partial differential equations with piecewise continuous arguments by Joseph Wiener, Lokenath Debnath

Subjects: “…partial differential equations…”
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A partial differential equation model of metastasized prostatic cancer by Avner Friedman, Harsh Vardhan Jain

“…Here, we develop a partial differential equation model of the growth and response to treatment of prostate cancer that has metastasized to the bone. …”
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Harmonic analysis and partial differential equations. Brief walk through these domains by Alejandro Ortiz Fernández

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On the Numerical Solution of Fractional Parabolic Partial Differential Equations with the Dirichlet Condition by Allaberen Ashyralyev, Zafer Cakir

“…A procedure of modified Gauss elimination method is used for solving these difference schemes in the case of one-dimensional fractional parabolic partial differential equations.…”
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The Interconnection Between Calculus of Variations, Partial Differential Equations and Differential Geometry by Delphin Mwinken

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Automatic Recognition of Financial Instruments Based on Anisotropic Partial Differential Equations by Wenfu Pan, Li Chen, Ruxing Zhang

“…In this paper, anisotropic partial differential equations are used to conduct an indepth study and analysis of automatic recognition of financial bills. …”
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Diffeomorphism neural operator for various domains and parameters of partial differential equations by Zhiwei Zhao, Changqing Liu, Yingguang Li, Zhibin Chen, Xu Liu

“…Abstract Solving partial differential equations (PDEs) across varying geometric domains and parameters represents a significant challenge in fields such as materials science, engineering, design and medical imaging, primarily due to the high computing cost associated with recomputing the solution for every change in geometry or parameters. …”
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