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Differential Equations, 2023
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Shishkina, E. L., Yusupova, A. K.
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Shishkina, E. L., Yusupova, A. K.
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Morphisms of the Heat Equation
Annals of Global Analysis and Geometry, 1997The author extends the Fuglede-Ishihara characterization of harmonic morphisms to maps \(f:M\times \mathbb{R}^+\to N\times \mathbb{R}^+\) that pull back local solutions of the heat equation on \(N\) to those of \(M\), as well as to maps \(f:M\times M\times \mathbb{R}^+\to N\times N\times \mathbb{R}^+\) that pull back the heat kernel of \(N\) to that of
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On Symmetries of the Heat Equation
Acta Applicandae Mathematicae, 1989Two aims are pursued in this article. The first one is methodological and consists of demonstrating the symmetry calculation techniques based on the commutation relation on the example of the quasi-linear heat equation. The second one consists of investigating the following open question: is the algebra of higher symmetries of the linear heat equation ...
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On a Universality of the Heat Equation
Mathematische Nachrichten, 1997AbstractWe prove that there are solutions u(t,x) of the heat equation ut = uxx such that every continuous function f : [a, b] → ℝ can be uniformly approximated by a subsequence of u (n, ·), nϵ ℕ.
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1998
Abstract We establish here two kinds of results. First, we show that if g satisfies certain conditions for |x| large, then all solutions of (5.1)-(5.3) are global. Then, in another spirit, some results prove that if g satisfies certain conditions for |x| small, then the solutions of (5.1)-(5.3) with small initial data are global.
Thierry Cazenave +2 more
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Abstract We establish here two kinds of results. First, we show that if g satisfies certain conditions for |x| large, then all solutions of (5.1)-(5.3) are global. Then, in another spirit, some results prove that if g satisfies certain conditions for |x| small, then the solutions of (5.1)-(5.3) with small initial data are global.
Thierry Cazenave +2 more
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2014
The problem of finding the steady state solution of the heat equation on the unit square, a basic example of the Dirichlet problem, is solved, and in the process ideas and theorems are developed, which are applicable to a broad range of mathematical problems.
Theodore Hromadka, Robert Whitley
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The problem of finding the steady state solution of the heat equation on the unit square, a basic example of the Dirichlet problem, is solved, and in the process ideas and theorems are developed, which are applicable to a broad range of mathematical problems.
Theodore Hromadka, Robert Whitley
openaire +1 more source