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49,226
USER’S GUIDE TO VISCOSITY SOLUTIONS OF SECOND ORDER PARTIAL DIFFERENTIAL EQUATIONS
, 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)
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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
STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS
"... The aim of these notes is to give an introduction to some aspects of the theory of Stochastic Partial Differential Equations. The focus will not be on generality but on presenting interesting and useful concepts in particular cases. First consider the SDE in Rd ..."
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The aim of these notes is to give an introduction to some aspects of the theory of Stochastic Partial Differential Equations. The focus will not be on generality but on presenting interesting and useful concepts in particular cases. First consider the SDE in Rd
Symmetries of Partial Differential Equations
 J. KOREAN MATH. SOC.
, 2003
"... We establish a link between the study of completely integrable systems of partial differential equations and the study of generic submanifolds in C n. Using the recent developments of CauchyRiemann geometry we provide the set of symmetries of such a system with a Lie group structure. Finally we d ..."
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Cited by 7 (4 self)
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We establish a link between the study of completely integrable systems of partial differential equations and the study of generic submanifolds in C n. Using the recent developments of CauchyRiemann geometry we provide the set of symmetries of such a system with a Lie group structure. Finally we
Solving Partial Differential Equations
, 1996
"... The paper deals with solving the partial differential equations by the old and well known "analog" method of lines. This method is also suitable for digital computation and it can be directly used for solving the time depending equations as e.g. heat and wave equations. The aim of the pape ..."
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The paper deals with solving the partial differential equations by the old and well known "analog" method of lines. This method is also suitable for digital computation and it can be directly used for solving the time depending equations as e.g. heat and wave equations. The aim
On Degenerate Partial Differential Equations
, 2010
"... Some of recent developments, including recent results, ideas, techniques, and approaches, in the study of degenerate partial differential equations are surveyed and analyzed. Several examples of nonlinear degenerate, even mixed, partial differential equations, are presented, which arise naturally i ..."
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Some of recent developments, including recent results, ideas, techniques, and approaches, in the study of degenerate partial differential equations are surveyed and analyzed. Several examples of nonlinear degenerate, even mixed, partial differential equations, are presented, which arise naturally
Renormalizing Partial Differential Equations
, 1994
"... We explain how to apply Renormalization Group ideas to the analysis of the longtime asymptotics of solutions of partial differential equations. We illustrate the method on several examples of nonlinear parabolic equations. We discuss many applications, including the stability of profiles and fronts ..."
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We explain how to apply Renormalization Group ideas to the analysis of the longtime asymptotics of solutions of partial differential equations. We illustrate the method on several examples of nonlinear parabolic equations. We discuss many applications, including the stability of profiles
Stochastic Partial Differential Equations driven by . . .
, 2004
"... In this paper we develop a white noise framework for the study of stochastic partial differential equations driven by a dparameter (pure jump) Lévy white noise. As an example we use this theory to solve the stochastic Poisson equation with respect to Lévy white noise for any dimension d. The soluti ..."
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Cited by 183 (8 self)
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In this paper we develop a white noise framework for the study of stochastic partial differential equations driven by a dparameter (pure jump) Lévy white noise. As an example we use this theory to solve the stochastic Poisson equation with respect to Lévy white noise for any dimension d
ARITHMETIC PARTIAL DIFFERENTIAL EQUATIONS
, 2006
"... We develop an arithmetic analogue of linear partial differential equations in two independent “spacetime” variables. The spatial derivative is a Fermat quotient operator, while the time derivative is the usual derivation. This allows us to “flow” integers or, more generally, points on algebraic gr ..."
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Cited by 6 (5 self)
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We develop an arithmetic analogue of linear partial differential equations in two independent “spacetime” variables. The spatial derivative is a Fermat quotient operator, while the time derivative is the usual derivation. This allows us to “flow” integers or, more generally, points on algebraic
Chaos in Partial Differential Equations
, 2002
"... Abstract. This is a survey on Chaos in Partial Differential Equations. First we classify soliton equations into three categories: 1. (1+1)dimensional soliton equations, 2. soliton lattices, 3. (1+n)dimensional soliton equations (n≥2). A systematic program has been established by the author and col ..."
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Cited by 4 (2 self)
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Abstract. This is a survey on Chaos in Partial Differential Equations. First we classify soliton equations into three categories: 1. (1+1)dimensional soliton equations, 2. soliton lattices, 3. (1+n)dimensional soliton equations (n≥2). A systematic program has been established by the author
Results 1  10
of
49,226