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Entropy and Partial Differential Equations

by Lawrence C. Evans - AMERICAN MATHEMATICAL SOCIETY, VOLUME , 1998
"... ..."
Abstract - Cited by 1497 (3 self) - Add to MetaCart
Abstract not found

USER’S GUIDE TO VISCOSITY SOLUTIONS OF SECOND ORDER PARTIAL DIFFERENTIAL EQUATIONS

by Michael G. Crandall, Hitoshi Ishii, Pierre-louis Lions , 1992
"... The notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems, existence theorems, and theorems about continuous dependence may now be proved by very efficient and striking argume ..."
Abstract - Cited by 1399 (16 self) - Add to MetaCart
The notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems, existence theorems, and theorems about continuous dependence may now be proved by very efficient and striking

The Wiener-Askey Polynomial Chaos for Stochastic Differential Equations

by Dongbin Xiu, George E M Karniadakis - SIAM J. SCI. COMPUT , 2002
"... We present a new method for solving stochastic differential equations based on Galerkin projections and extensions of Wiener's polynomial chaos. Specifically, we represent the stochastic processes with an optimum trial basis from the Askey family of orthogonal polynomials that reduces the dime ..."
Abstract - Cited by 398 (42 self) - Add to MetaCart
We present a new method for solving stochastic differential equations based on Galerkin projections and extensions of Wiener's polynomial chaos. Specifically, we represent the stochastic processes with an optimum trial basis from the Askey family of orthogonal polynomials that reduces

Analysis of Fractional Differential Equations

by Kai Diethelm, Neville J. Ford , 1999
"... We discuss existence, uniqueness and structural stability of solutions of nonlinear dierential equations of fractional order. The dierential operators are taken in the Riemann-Liouville sense and the initial conditions are specied according to Caputo's suggestion, thus allowing for interpretati ..."
Abstract - Cited by 205 (4 self) - Add to MetaCart
We discuss existence, uniqueness and structural stability of solutions of nonlinear dierential equations of fractional order. The dierential operators are taken in the Riemann-Liouville sense and the initial conditions are specied according to Caputo's suggestion, thus allowing

FUCHSIAN DIFFERENTIAL EQUATIONS

by Toshio Oshima , 2011
"... and Fuchsian differential equations ..."
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and Fuchsian differential equations

Numerical Integration of Stochastic Differential Equations

by G. N. Milstein, M. V. Tretyakov , 1995
"... Abstract. We propose a new concept which allows us to apply any numerical method of weak approximation to a very broad class of stochastic differential equations (SDEs) with nonglobally Lipschitz coefficients. Following this concept, we discard the approximate trajectories which leave a sufficiently ..."
Abstract - Cited by 200 (12 self) - Add to MetaCart
Abstract. We propose a new concept which allows us to apply any numerical method of weak approximation to a very broad class of stochastic differential equations (SDEs) with nonglobally Lipschitz coefficients. Following this concept, we discard the approximate trajectories which leave a

Modeling Gene Expression With Differential Equations

by Ting Chen, Hongyu L. He, George M. Church - PAC. SYMP. BIOCOMPUT , 1999
"... ..."
Abstract - Cited by 241 (1 self) - Add to MetaCart
Abstract not found

Mean-field backward stochastic differential equations and related patial differential equations

by Rainer Buckdahn, Juan Li, Shige Peng , 2007
"... In [5] the authors obtained Mean-Field backward stochastic differential equations (BSDE) associated with a Mean-field stochastic differential equation (SDE) in a natural way as limit of some highly dimensional system of forward and backward SDEs, corresponding to a large number of “particles” (or “a ..."
Abstract - Cited by 181 (14 self) - Add to MetaCart
In [5] the authors obtained Mean-Field backward stochastic differential equations (BSDE) associated with a Mean-field stochastic differential equation (SDE) in a natural way as limit of some highly dimensional system of forward and backward SDEs, corresponding to a large number of “particles” (or

• Linearity of Differential Equations

by unknown authors
"... • First order ordinary differential equation ..."
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• First order ordinary differential equation

DIFFERENTIAL EQUATIONS

by Boris Doubrov
"... The geometric approach to the study of differential equations goes back to Sophus Lie and Elie Cartan. According to the modern inter-pretation of this approach, based on the notion ofjet space, we consider a differential equation as a submanifold in the jet space with induced geometric structure. Us ..."
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The geometric approach to the study of differential equations goes back to Sophus Lie and Elie Cartan. According to the modern inter-pretation of this approach, based on the notion ofjet space, we consider a differential equation as a submanifold in the jet space with induced geometric structure
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