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CFD analysis of heat and mass transfer in hollow fiber DCMD enhanced by metal foam. [PDF]
Abrofarakh M +3 more
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Darboux transformations and linear parabolic partial differential equations
Journal of Physics A: Mathematical and General, 2002Summary: Solutions for a class of linear parabolic partial differential equation are provided. These solutions are obtained by first solving a system of (\(n + 1\)) nonlinear partial differential equations. This system arises as the coefficients of a Darboux transformation and is equivalent to a matrix Burgers' equation.
Arrigo, Daniel J., Hickling, Fred
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Parabolic Partial Differential Equations
1997In Chapter 2, Section 2.2, we showed how one can start with a transition probability function P(s, x; t, ·) and end up with a Markov process. The problem is: where does P(s, x; t, ·) come from? The example we gave there, namely: $$ P(s,x;t,\Gamma ) = \int\limits_\Gamma {g_d } \left( {t - s,y - x} \right)dy $$ (11) is a natural one from the ...
Daniel W. Stroock +1 more
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Hypergeometric Functions and Parabolic Partial Differential Equations
Journal of Dynamical and Control Systems, 2005zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Parabolic partial differential equations
1995We now describe how to apply the finite element to parabolic partial differential equations. This is done by approximating the parabolic partial differential equation by either a sequence of ordinary differential equations or a sequence of elliptic partial differential equations.
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Partial differential equations II — parabolic equations
1986The simplest parabolic differential equation is (6.3) or, as we normally meet it, (6.3a): $$\frac{{\partial u}}{{\partial t}} = a\frac{{{\partial ^2}u}}{{\partial {x^2}}}$$ (7.1) in which u is given as a function of a space variable x and of time t, and in which the coefficient a is a constant.
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Partial Differential Equations of Parabolic Type
2004In the present chapter we consider the well-posedness of an abstract Cauchy problem for differential equations of parabolic type, $$v'(t) + A(t)v(t) = f(t)(0 \leqslant t \leqslant T),v(0) = {{v}_{0}}$$ in an arbitrary Banach space with the linear positive operators A(t).
Allaberen Ashyralyev +1 more
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