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MathematicsThe paper studies an unsteady equation with quadratic nonlinearity in second derivatives, that occurs in electron magnetohydrodynamics. In mathematics, such PDEs are referred to as parabolic Monge–Ampère equations. An overview of the Monge–Ampère type equations is given, in which their unusual qualitative features are noted. For the first time, the Lie
A D Polyanin +2 more
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F-Operators for the Construction of Closed Form Solutions to Linear Homogenous PDEs with Variable Coefficients [PDF]
Mathematics, 2021 A computational framework for the construction of solutions to linear homogenous partial differential equations (PDEs) with variable coefficients is developed in this paper. The considered class of PDEs reads: ∂p∂t−∑j=0m∑r=0njajrtxr∂jp∂xj=0 F-operators are introduced and used to transform the original PDE into the image PDE.
Zenonas Navickas +2 more
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Determinism, well-posedness, and applications of the ultrahyperbolic wave equation in spacekime
Partial Differential Equations in Applied Mathematics, 2022 Spatiotemporal dynamics of many natural processes, such as elasticity, heat propagation, sound waves, and fluid flows are often modeled using partial differential equations (PDEs).
Yuxin Wang +3 more
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MethodsX, 2023 The analysis of nonlinear elliptic PDEs representing stationary convection-dominated diffusion equation, Sine-Gordon equation, Helmholtz equation, and heat exchange diffusion model in a battery often lacks in closed-form solutions.
Navnit Jha, Bhagat Singh
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Applied Sciences, 2022 The current article explains the 3-D MHD fluid flow under the impact of a magnetic field with an inclined angle. The porous sheet is embedded in the flow of a fluid to yield the better results of the problem.
Angadi Basettappa Vishalakshi +3 more
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Heliyon, 2023 Present study is dedicated to analyze the closed form solution of nanofluid flow over a stretching/shrinking sheet with dual availability. Flow is developed through two-dimensional boundary layer theory.
Rizwan Ul Haq +2 more
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Propulsion and Power Research, 2023 It is increasingly apparent that the inclusion of mass transfer aspects, together with certain thermal conditions, in the momentum and energy equations governing MHD flows leads to a numbers of real life applications.
Naveen Dwivedi +2 more
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Coupling Chemotaxis and Growth Poromechanics for the Modelling of Feather Primordia Patterning
Mathematics, 2022 In this paper we propose a new mathematical model for describing the complex interplay between skin cell populations with fibroblast growth factor and bone morphogenetic protein, occurring within deformable porous media describing feather primordia ...
Nicolás A. Barnafi +3 more
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Scientific Reports, 2022 The paper aims to investigate the channel flow of second grade visco-elastic fluid generated due to an oscillating wall. The effect of heat and mass transfer has been taken into account. The phenomenon has been modelled in terms of PDEs. The constitutive
Zahid Khan +3 more
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Mathematics, 2020 In the paper, we consider geodesic mappings of spaces with an affine connections onto generalized symmetric and Ricci-symmetric spaces. In particular, we studied in detail geodesic mappings of spaces with an affine connections onto 2-, 3-, and m- (Ricci-)
Volodymyr Berezovski +3 more
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