Results 1 to 10 of about 6,545,148 (269)
A Characteristic Equation for Non-autonomous Partial Functional Differential Equations
Journal of Differential Equations, 2002 Using the evolution semigroup approach, the authors give a characterization of exponential stability for the nonautonomous partial functional-differential equation \[ \dot{u}(t) = A(t) u(t) + L(t) u_t,\quad t \geq s, \qquad u(t) = \varphi(t-s),\quad s-r \leq t \leq s, \] in terms of a generalized characteristic equation which is formulated on adequate ...
Roland Schnaubelt, Frank Räbiger
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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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Functional analysis and partial differential equations
Mathematische Annalen, 1959 Felix E Browder
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Neural Partial Differential Equations with Functional Convolution
CoRR, 2023 10 pages of main text, 7 pages of appendix, 7 figures in main ...
Ziqian Wu +6 more
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Existence and stability for partial functional differential equations [PDF]
Transactions of the American Mathematical Society, 1974 Publisher Summary This chapter discusses the existence and stability for a class of partial functional differential equations. As a model for this class, one may take the equation wt(x, t) = wxx (x, t) + ƒ(t, w(x, t − r)), 0 ≤ x ≤ Π, t ≥ 0, w(0, t) = w(Π, t) = 0, t ≥ 0, w(x, t) = Φ (x, t), 0 ≤ x ≤ Π, −r ≤ t ≤ 0, where ƒ is a linear or nonlinear ...
Travis, C. C., Webb, G. F.
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Quasilinear Parabolic Equations Associated with Semilinear Parabolic Equations
Mathematics, 2023 We formulate a quasilinear parabolic equation describing the behavior of the global-in-time solution to a semilinear parabolic equation. We study this equation in accordance with the blow-up and quenching patterns of the solution to the original ...
Katsuyuki Ishii +2 more
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On a Nonlocal Problem for Mixed-Type Equation with Partial Riemann-Liouville Fractional Derivative
Fractal and Fractional, 2022 The present paper presents a study on a problem with a fractional integro-differentiation operator in the boundary condition for an equation with a partial Riemann-Liouville fractional derivative. The unique solvability of the problem is proved.
Menglibay Ruziev, Rakhimjon Zunnunov
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Predictor control for non‐linear systems actuated via counter‐convecting transport PDEs
IET Control Theory & Applications, 2021 The authors investigate predictor control for the cascaded system of a non‐linear ordinary differential equation with counter‐convecting transport partial differential equations with propagation velocities dependent on partial differential equations ...
Xiushan Cai +3 more
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On the Tonelli method for the degenerate parabolic Cauchy problem with functional argument [PDF]
Opuscula Mathematica, 2014 The degenerate parabolic Cauchy problem is considered. A functional argument in the equation is of the Hale type. As a limit of piecewise classical solutions we obtain a viscosity solution of the main problem. Presented method is an adaptation of Tonelli'
Krzysztof A. Topolski
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Partial Differential Equations and Function Spaces [PDF]
Journal of Function Spaces, 2016 It is well known that PDEs and the theory of function spaces have played a central role in the mathematical analysis of problems arising from mathematical physics, biology, and other branches of modern applied sciences. This special issue addresses the current advances in these two broad areas; in particular it focuses on the connections and ...
Shijun Zheng +3 more
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