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Complex Partial Differential Equations
Journal of Mathematical ScienceszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Aksoy, Ü. +3 more
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Deep Neural Networks Motivated by Partial Differential Equations
Journal of Mathematical Imaging and Vision, 2018Partial differential equations (PDEs) are indispensable for modeling many physical phenomena and also commonly used for solving image processing tasks.
Lars Ruthotto, E. Haber
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Differential games with partial differential equations
1975Examples of differential games are given, where the state equation is a partial differential equation. They can be solved explicitly and show clearly how the values of the control functions enter in the solution. This enables us to set up a method of solving these games, which should also be applied to more complicated differential games, complementing
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Stochastic partial differential equations
2014Second order stochastic partial differential equations are discussed from a rough path point of view. In the linear and finite-dimensional noise case we follow a Feynman–Kac approach which makes good use of concentration of measure results, as those obtained in Sect. 11.2.
Peter K. Friz, Martin Hairer
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On The Factorization of Partial Differential Equations
Canadian Journal of Mathematics, 1987In [4] N. Steinmetz used Nevanlinna theory to establish remarkably versatile theorems on the factorization of ordinary differential equations which implied numerous previous results of various authors. (Here factorization is taken in the sense of function composition as introduced by F.
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Partial differential equations
2020This chapter discusses partial differential equations (PDEs). It begins by presenting elementary cases of PDEs, which highlights that PDEs give rise to 'functions of integration', in contrast to ordinary differential equations (ODEs), which have 'constants of integration'.
D.S. Sivia, J.L. Rhodes, S.G. Rawlings
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On Elliptic Partial Differential Equations
2011This series of lectures will touch on a number of topics in the theory of elliptic differential equations. In Lecture I we discuss the fundamental solution for equations with constant coefficients. Lecture 2 is concerned with Calculus inequalities including the well known ones of Sobolev. In lectures 3 and 4 we present the Hilbert space approach to the
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Partial Differential Equations II
2002Partial differential equations of the form $$k{\partial \over {\partial t}}u(r,t) = \nabla ^2 u(r,t)$$ (diffusion equation) and $${{\partial ^2 } \over {\partial t^2 }}u(r,t) = c^2 \nabla ^2 u(r,t)$$ (wave equation) are amenable to the use of the Laplace transform.1 Indeed, on taking the Laplace transform of the former, we get ...
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Optimal Control of Partial Differential Equations
Applied Mathematical Sciences, 2021A. Manzoni, A. Quarteroni, S. Salsa
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Quantized Partial Differential Equations
2004This book contains three chapters and two addenda. Quantized PDE's.I. In this first part we consider quantum (super) manifolds as topological spaces locally identified with open sets of some locally convex topological vector spaces built starting from suitable topological algebras $A$, \textit{quantum (super)algebras}.
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