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Partial Differential Equations and Difference Equations
Proceedings of the American Mathematical Society, 1965(1. 1) Pi(alax)y = ? (1 _ i _ m) where x = (x1, * , xn), a/ax = (a/ax1, *, O/0xn). The Pi's are assumed to be homogeneous polynomials with real coefficients. The term solution is used to include the generalized solutions. A generalized solution is any function continuous on R which is a uniform limit on compact subsets of CX solutions (see [2, p. 65]).
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On uncertain partial differential equations
Fuzzy Optimization and Decision Making, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Pseudoparabolic Partial Differential Equations
SIAM Journal on Mathematical Analysis, 1970This is the publisher’s final pdf. The published article is copyrighted by the Society for Industrial and Applied Mathematics and can be found at: http://epubs.siam.org/loi/sjmaah.
Showalter, R. E., Ting, T. W.
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ON STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS
Mathematics of the USSR-Sbornik, 1975In this paper we consider the Cauchy problem for second-order stochastic partial differential equations of parabolic type. We study linear and nonlinear equations for filtering Markov diffusion processes. Theorems on the existence, uniqueness and smoothness of solutions are proved.Bibliography: 21 items.
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Differential games with partial differential equations
1975Examples of differential games are given, where the state equation is a partial differential equation. They can be solved explicitly and show clearly how the values of the control functions enter in the solution. This enables us to set up a method of solving these games, which should also be applied to more complicated differential games, complementing
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Stochastic partial differential equations
2014Second order stochastic partial differential equations are discussed from a rough path point of view. In the linear and finite-dimensional noise case we follow a Feynman–Kac approach which makes good use of concentration of measure results, as those obtained in Sect. 11.2.
Peter K. Friz, Martin Hairer
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A Differentiation Index for Partial Differential-Algebraic Equations
SIAM Journal on Scientific Computing, 2000Summary: A differentiation index for nonlinear partial differential-algebraic equations is presented. Determination of the differentiation index with respect to a direction in the space of independent variables uncovers all equations that must be satisfied by the Cauchy data on the hyperplane orthogonal to that direction.
Wade S. Martinson, Paul I. Barton
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On The Factorization of Partial Differential Equations
Canadian Journal of Mathematics, 1987In [4] N. Steinmetz used Nevanlinna theory to establish remarkably versatile theorems on the factorization of ordinary differential equations which implied numerous previous results of various authors. (Here factorization is taken in the sense of function composition as introduced by F.
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Similarity Transformations for Partial Differential Equations
SIAM Review, 1998The special forms of Lie group transformations, such as scaling, translation and the spiral group are used to find the so-called similarity solutions to a couple of basic equations in mathematical physics, namely, the wave equation in mechanics and the boundary layer equation in fluid mechanics.
Mehmet Pakdemirli, Muhammet Yürüsoy
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On arithmetic partial differential equations
J. Integer Seq., 2016Summary: \textit{J. Kovič} [J. Integer Seq. 15, No. 3, Article 12.3.8, 16 p. (2012; Zbl 1291.11009)], and implicitly \textit{V. Ufnarovski} and \textit{B. Åhlander} [J. Integer Seq. 6, No. 3, Art. 03.3.4, 24 p. (2003; Zbl 1142.11305)], defined a notion of arithmetic partial derivative. We generalize the definition for rational numbers and study several
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