A decomposition theorem for solutions of parabolic equations.

Watson, N.A.

Displaying similar documents to “A decomposition theorem for solutions of parabolic equations.”

A remark on the uniqueness of fundamental solutions to the $p$ -Laplacian equation, $p > 2$ .

Laurençot, Ph. (1998)

Portugaliae Mathematica

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Sets of determination for parabolic functions on a half-space

Jarmila Ranošová (1994)

Commentationes Mathematicae Universitatis Carolinae

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We characterize all subsets $M$ of $ℝ^{n} \times ℝ^{+}$ such that $sup_{X \in ℝ^{n} \times ℝ^{+}} u (X) = sup_{X \in M} u (X)$ for every bounded parabolic function $u$ on $ℝ^{n} \times ℝ^{+}$ . The closely related problem of representing functions as sums of Weierstrass kernels corresponding to points of $M$ is also considered. The results provide a parabolic counterpart to results for classical harmonic functions in a ball, see References. As a by-product the question of representability of probability continuous distributions as sums of multiples of normal distributions is investigated. ...

Existence and asymptotic behaviour of positive solutions for some nonlinear parabolic systems in the half-space.

Ghanmi, Abdeljabbar, Toumi, Faten (2011)

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

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Regularity and uniqueness in quasilinear parabolic systems

Pavel Krejčí, Lucia Panizzi (2011)

Applications of Mathematics

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Inspired by a problem in steel metallurgy, we prove the existence, regularity, uniqueness, and continuous data dependence of solutions to a coupled parabolic system in a smooth bounded 3D domain, with nonlinear and nonhomogeneous boundary conditions. The nonlinear coupling takes place in the diffusion coefficient. The proofs are based on anisotropic estimates in tangential and normal directions, and on a refined variant of the Gronwall lemma.

Characterization of sets of determination for parabolic functions on a slab by coparabolic (minimal) thinness

Jarmila Ranošová (1996)

Commentationes Mathematicae Universitatis Carolinae

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Let $T$ be a positive number or $+ \infty$ . We characterize all subsets $M$ of $ℝ^{n} \times] 0, T [$ such that $inf_{X \in ℝ^{n} \times] 0, T [} u (X) = inf_{X \in M} u (X) i$ for every positive parabolic function $u$ on $ℝ^{n} \times] 0, T [$ in terms of coparabolic (minimal) thinness of the set $M_{δ} = \cup_{(x, t) \in M} B^{p} ((x, t), δ t)$ , where $δ \in (0, 1)$ and $B^{p} ((x, t), r)$ is the “heat ball” with the “center” $(x, t)$ and radius $r$ . Examples of different types of sets which can be used instead of “heat balls” are given. It is proved that (i) is equivalent to the condition ${sup}_{X \in ℝ^{n} \times ℝ^{+}} u (X) = {sup}_{X \in M} u (X)$ for every bounded parabolic function on $ℝ^{n} \times ℝ^{+}$ and hence to all equivalent conditions given in the article...

Displaying similar documents to “A decomposition theorem for solutions of parabolic equations.”

A remark on the uniqueness of fundamental solutions to the p -Laplacian equation, p > 2 .

Sets of determination for parabolic functions on a half-space

Existence and asymptotic behaviour of positive solutions for some nonlinear parabolic systems in the half-space.

Regularity and uniqueness in quasilinear parabolic systems

Characterization of sets of determination for parabolic functions on a slab by coparabolic (minimal) thinness

A remark on the uniqueness of fundamental solutions to the $p$ -Laplacian equation, $p > 2$ .