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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.
Andrei D. Polyanin, Alexander V. Aksenov
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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.
Navickas, Zenonas +4 more
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A new technique in constructing closed‐form solutions for nonlinear PDEs appearing in fluid mechanics and gas dynamics [PDF]
Mathematical Problems in Engineering, 1996 We develop a new unique technique in constructing closed‐form solutions for several nonlinear partial differential systems appearing in fluid mechanics and gas dynamics. The obtained solutions include fewer arbitrary functions than needed for general solutions, fact that permits us to specify them according to the initial state, or the geometry, of ...
D.E. Panayotounakos
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Computers & Mathematics with Applications, 2017 Fluorescence recovery after photobleaching (FRAP) is a widely used method to analyze (usually using fluorescence microscopy) the mobility of either fluorescently tagged or autofluorescent (e.g.,photosynthetic) proteins in living cells. The FRAP method resides in imaging the recovery of fluorescence intensity over time in a region of interest previously
Papáček, Š. +2 more
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Existence of dual solution for MHD boundary layer flow over a stretching/shrinking surface in the presence of thermal radiation and porous media: KKL nanofluid model [PDF]
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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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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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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