Results 301 to 310 of about 235,217 (374)

Parabolic Partial Differential Equations

1997
In 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, S. R. Srinivasa Varadhan   +1 more
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Deep Learning-Based Numerical Methods for High-Dimensional Parabolic Partial Differential Equations and Backward Stochastic Differential Equations

Communications in Mathematics and Statistics, 2017
We study a new algorithm for solving parabolic partial differential equations (PDEs) and backward stochastic differential equations (BSDEs) in high dimension, which is based on an analogy between the BSDE and reinforcement learning with the gradient of ...
Weinan E, Jiequn Han, Arnulf Jentzen
semanticscholar   +1 more source

Hypergeometric Functions and Parabolic Partial Differential Equations

Journal of Dynamical and Control Systems, 2005
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Controllability for Partial Differential Equations of Parabolic Type

SIAM Journal on Control, 1974
The purpose of this paper is to study questions regarding controllability for the distributed-parameter systems described by partial differential equations of parabolic type. Fattorini [2]–[4] studied controllability by finitely many functions of time.
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A Method of Ascent for Parabolic and Pseudoparabolic Partial Differential Equations

SIAM Journal on Mathematical Analysis, 1976
This paper extends the idea of a method of ascent as developed by Gilbert for elliptic equations and Colton for pseudoparabolic equations. We develop a method of ascent for parabolic equations and extend Colton’s results for the pseudoparabolic case.
Rundell, William, Stecher, Michael
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Partial Differential Equations of Parabolic Type

2004
In 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, Pavel E. Sobolevskii   +1 more
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Partial differential equations II — parabolic equations

1986
The 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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OSCILLATION OF A CLASS OF PARABOLIC PARTIAL FUNCTIONAL DIFFERENTIAL EQUATIONS

Acta Mathematica Scientia, 1993
The authors study oscillation phenomena for the partial functional differential equation \[ \delta/ \delta t \left[u- \sum^ m_{i=1} c_ i(t) u(s,t-r_ i)\right] = a(t) \Delta u - p(x,t)u - \int^ b_ a q(x,t, \zeta) u \bigl( x,g (t, \zeta) \bigr) d \sigma (\zeta), \] \((x,t) \in \Omega \times [0,\infty)\), where \(\Omega\) is a bounded domain in \(\mathbb ...
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On regular and parabolic systems of partial differential equations.

1957
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Computational study for a class of time-dependent singularly perturbed parabolic partial differential equation through tension spline

Computational and Applied Mathematics, 2020
P. M. Kumar, A. Kanth
semanticscholar   +1 more source