Linear partial differential equation
On Symbolic Solutions of Algebraic Partial Differential Equations
... The second equation is linear and separable but depends on the solution of the first. The first ODE can be solved independently. Its solution s(t) = η(t, k) will depend on an arbitrary constant k. Hence, ...
12
On complex singularity analysis for some linear partial differential equations in C3
... 𝜑 𝛼,𝑛 0 ,𝑛 1 ,(𝑙 ℎ ) 0≤ℎ≤𝛼 ≤ 𝜓 𝛼,𝑛 0 ,𝑛 1 ,(𝑙 ℎ ) 0≤ℎ≤𝛼 (4) for any nonnegative integers 𝛼, 𝑛 0 , 𝑛 1 , 𝑙 ℎ with 0 ≤ ℎ ≤ 𝛼 and whose generating formal series satisfies some integrod- ifferential functional ...
31
On the multiple scale analysis for some linear partial q difference and differential equations with holomorphic coeffcients
... Two singularly perturbed terms on the right-hand side of equation (1.1) are distin- guished. This makes a crucial difference with respect to the previous work [7], in which only one term appears, whilst the ...
42
Partial Differential Equations with MATLAB
... We also treat in this chapter the PDE analogs of other ideas that were studied in ODEs: initial and boundary conditions, and the important concept of a linear PDE. We then introduce one of the most important tools ...
670
Chaotic semigroups from second order partial differential equations
... the linear telegraph equation on an infinite transmission lossless ...This equation is obtained from a system of two coupled differential equations that represent the voltage and current on an ...
9
Strongly regular multi level solutions of singularly perturbed linear partial differential equations
... In the previous section, we have observed (Theorem 3 and Theorem 4) a different behavior of the difference of two adjacent solutions, depending on the geometry of the problem and the nature of the elements appearing in ...
30
Differential Equation schaum's.pdf
... of partial fractions transforms a function of the form a(s) /b(s), where both a(s) and b(s) are polynomials in s, into the sum of other fractions such that the denominator of each new fraction is either a ...
143
Revisiting university students’ knowledge that involves basic differential equation questions
... a differential equation is reduced to the application of proper solu- tion methods to a certain type of equation differential ...Keywords: Differential equations; Meaning; ...
11
A nonlinear ordinary differential equation associated with the quantum sojourn time
... ordinary differential equation on the half-line, with the Dirichlet boundary condition at the ...This equation arises when studying the local maxima of the sojourn time for a free quantum particle ...
16
On Gevrey solutions of threefold singular nonlinear partial differential equations
... for partial differential equations which are singular, as far as we know no treatment can be found in the literature dealing with a singularly perturbed partial differential equation which additionally ...
28
Non linear incentive equilibrium strategies for a transboundary pollution differential game
... This paper is a follow-up of De Frutos & Mart´ın-Herr´an (2015) and assumes state-dependent and decision-dependent equilibrium strategies defined as non-linear functions of the control variables of both ...
17
A C++ Class for Analyzing Vector Boolean Functions from a Cryptographic Perspective
... Spectrum, Linear Profile, Differential Profile and Autocorrelation ...as linear structures, linear potential, differential potential and the maximum possible nonlinearity or linearity ...
9
A Lie Deprit perturbation algorithm for linear differential equations with periodic coefficients
... Here F and P are n × n matrices, P (t) = P (t + T ) for all t and F is constant. As a matter of fact, this theorem combines two propositions. On the one hand, it provides a general statement about the structure of the ...
18
How important are internal temperature gradients in french straws during freezing of bovine sperm in nitrogen vapor?
... conduction equation with phase change transition a new mathematical formulation of the apparent specific heat curve was applied using Heaviside and Gaussian functions; this method has been described in detail in ...
9
new contributions to non linear process monitoring through kernel partial least squares
... the linear PLSR approach is preferable when the model would mainly be used for monitoring purposes; and ii) the nonlinear KPLS approach is preferable when the model would mainly be used for prediction ...
27
On parametric Gevrey asymptotics for singularly perturbed partial differential equations with delays
... gous equation as the one studied in the previous section, written as a formal power series in 𝑧 with coefficients in an appropriate Banach space of functions in the variable 𝜏 and the perturbation parameter ...
19
Sparse differential resultant formulas: between the linear and the nonlinear case
... Using the previous results, a family of systems F of generic sparse differential polynomials can be obtained, so that degree bounds of the sparse differential resultant can be given in terms of mixed volumes. In [4], such ...
6
Slow fast n dimensional piecewise linear differential systems
... In this paper we have done a next step towards a systematic study of slow-fast dynamics in a piecewise linear setting. An explicit expression for the slow manifold have been derived. This expression allows to find ...
34
Gevrey multiscale expansions of singular solutions of PDEs with cubic nonlinearity
... nonlinear partial differential equations. In the framework of linear PDEs, the case of so- called Fuchsian or regular singularity in one complex variable is a well understood subject until the ...
89
Regular optimal control problems with quadratic final penalties
... the linear-quadratic regulator (LQR) case there exist well- known methods (see for instance [4], [24]) to transform the boundary-value into a final-value problem, related to the differential Riccati ...
14