Transcendental entire solutions of several general quadratic type PDEs and PDDEs in $ \mathbb{C}^2 $ [PDF]
, 2022 The functional equations $ f^2+g^2=1 $ and $ f^2+2αfg+g^2=1 $ are respectively called Fermat-type binomial and trinomial equations. It is of interest to know about the existence and form of the solutions of general quadratic functional equations. Utilizing Nevanlinna's theory for several complex variables, in this paper, we study the existence and form
Molla Basir Ahamed, Sanju Mandal
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Real eternal PDE solutions are not complex entire: a quadratic parabolic example [PDF]
Journal of Elliptic and Parabolic EquationsAbstract In parabolic or hyperbolic PDEs, solutions which remain uniformly bounded for all real times $$t=r\in \mathbb {R}$$ t = r ∈ R
Bernold Fiedler, Hannes Stuke
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On the growth of positive entire solutions of elliptic PDEs and their gradients
Discrete & Continuous Dynamical Systems - S, 2014 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Antonio Vitolo
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A fast quantum algorithm for solving partial differential equations [PDF]
Scientific ReportsThe numerical solution of partial differential equations (PDEs) is essential in computational physics. Over the past few decades, various quantum-based methods have been developed to formulate and solve PDEs.
Azim Farghadan +2 more
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Meromorphic solutions of generalized inviscid Burgers’ equations and related PDES
Comptes Rendus. Mathématique, 2021 The purposes of this paper are twofold. The first one is to describe entire solutions of certain type of PDEs in $\mathbb{C}^n$ with the modified KdV-Burgers equation and modified Zakharov-Kuznetsov equation as the prototypes.
Lü, Feng
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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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Heliyon, 2023 This article aims to investigate the analytical nature and approximate solution of the radiated flow of electrically conductive viscous fluid into a porous medium with slip effects (RFECVF).
Muhammad Shoaib +8 more
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Open Mathematics, 2023 Our purpose in this article is to describe the solutions of several product-type nonlinear partial differential equations (PDEs) (a1u+b1uz1+c1uz2)(a2u+b2uz1+c2uz2)=1,\left({a}_{1}u+{b}_{1}{u}_{{z}_{1}}+{c}_{1}{u}_{{z}_{2}})\left({a}_{2}u+{b}_{2}{u}_{{z}_{
Xu Yi Hui +3 more
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Pointwise estimates and rigidity results for entire solutions of nonlinear elliptic pde’s [PDF]
ESAIM: Control, Optimisation and Calculus of Variations, 2013 We prove pointwise gradient bounds for entire solutions of pde’s of the form ℒu(x) = ψ(x, u(x), ∇u(x)) ,where ℒ is an elliptic operator (possibly singular or degenerate). Thus, we obtain some Liouville type rigidity results. Some classical results of J. Serrin are also recovered as particular cases of our approach.
A. Farina, E. Valdinoci
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Exact solutions of linear reaction-diffusion processes on a uniformly growing domain: criteria for successful colonization. [PDF]
PLoS ONE, 2015 Many processes during embryonic development involve transport and reaction of molecules, or transport and proliferation of cells, within growing tissues.
Matthew J Simpson
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