Displaying similar documents to “Cauchy problem for a class of parabolic systems of Shilov type with variable coefficients”

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 × ℝ + such that sup X ∈ ℝ n × ℝ + u ( X ) = sup X ∈ M u ( X ) for every bounded parabolic function u on ℝ n × 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. ...

On the asymptotic behavior of solutions of second order parabolic partial differential equations

Wei-Cheng Lian, Cheh-Chih Yeh (1996)

Annales Polonici Mathematici

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We consider the second order parabolic partial differential equation    ∑ i , j = 1 n a i j ( x , t ) u x i x j + ∑ i = 1 n b i ( x , t ) u x i + c ( x , t ) u - u t = 0 . Sufficient conditions are given under which every solution of the above equation must decay or tend to infinity as |x|→ ∞. A sufficient condition is also given under which every solution of a system of the form    L α [ u α ] + ∑ β = 1 N c α β ( x , t ) u β = f α ( x , t ) , where    L α [ u ] ≡ ∑ i , j = 1 n a i j α ( x , t ) u x i x j + ∑ i = 1 n b i α ( x , t ) u x i - u t , must decay as t → ∞.