Results 11 to 20 of about 2,559 (253)
Machine Learning and Knowledge Extraction, 2020 This article presents a new methodology called Deep Theory of Functional Connections (TFC) that estimates the solutions of partial differential equations (PDEs) by combining neural networks with the TFC.
Carl Leake, Daniele Mortari
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Stochastic PDEs via convex minimization [PDF]
Communications in Partial Differential Equations, 2020 We prove the applicability of the Weighted Energy-Dissipation (WED) variational principle to nonlinear parabolic stochastic partial differential equations in abstract form.
Luca Scarpa, U. Stefanelli
semanticscholar +3 more sources
Monotone heteroclinic solutions to semilinear PDEs in cylinders and applications [PDF]
Calculus of Variations and Partial Differential EquationsIn this paper we show the existence of strictly monotone heteroclinic type solutions of semilinear elliptic equations in cylinders. The motivation of this construction is twofold: first, it implies the existence of an entire bounded solution of a ...
Fabio De Regibus, David Ruiz
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Form of solutions to quadratic trinomial partial differential equations with two complex variables
Electronic Journal of Differential EquationsThis article describes the from of entire solutions to quadratic trinomial partial differential equations (PDEs). By applying the Nevanlinna theory and the characteristic equation of PDEs, we extend some of the results obtained in [24].
J. Tu, Huizheng Wei
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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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Transcendental entire solutions of several general quadratic type PDEs and PDDEs in $ \mathbb{C}^2 $
, 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
Ahamed, Molla Basir, Mandal, Sanju
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Analysis of Systems of Hyperbolic Partial Differential Equations Coupled to Switched Differential Algebraic Equations [PDF]
, 2021 Simplified ODE models describing blood flow rate are governed by the pressure gradient. However, assuming the orientation of the blood flow in a human body correlates to a positive direction, a negative pressure gradient forces the valve to shut, which
Kocoglu, Damla
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Optimal Control of Quasilinear Parabolic PDEs: Theory and Numerics [PDF]
, 2022 This thesis is concerned with theory and numerics of optimal control of quasilinear parabolic PDEs. The underlying parabolic PDE models, e.g., heat conduction with temperature-dependent thermal conductivity and is highly nonlinear with a nonmonotone ...
Hoppe, Fabian
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The class of Clifford-Fourier transforms [PDF]
, 2011 Recently, there has been an increasing interest in the study of hypercomplex signals and their Fourier transforms. This paper aims to study such integral transforms from general principles, using 4 different yet equivalent definitions of the classical ...
De Bie, Hendrik +5 more
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Contributions to Nonlinear PDEs arising in Conformal Geometry, Mean Field Games and Choquard models. [PDF]
, 2023 The goal of this thesis is to analyze certain nonlinear elliptic Partial Differential Equations (briefly PDEs) that arise in Conformal Geometry, Mean Field Games theory, and Choquard models.
BERNARDINI, CHIARA
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