In this paper, we study the large time behavior of solutions of the parabolic semilinear equation δtu-div（a（x）△↓u） = -｜u｜^αu in （0,∞） × R^N, where α 〉 0 is constant and a∈ Cb^1（R^N） is a symmetr...In this paper, we study the large time behavior of solutions of the parabolic semilinear equation δtu-div（a（x）△↓u） = -｜u｜^αu in （0,∞） × R^N, where α 〉 0 is constant and a∈ Cb^1（R^N） is a symmetric periodic matrix satisfying some ellipticity assumptions.Considering an integrable initial data u0 and α ∈ （2/N, 3/N）, we prove that the large time behavior of solutions is given by the solution U（t, x） of the homogenized linear problem δtU-div（a^h△↓U）=0,U（0） = C, where a^h is the homogenized matrix of a（x）, C is a positive constant and δ is the Dirac measure at 0.展开更多
This paper tries to utilize the methods of stochastic analysis and matrix analysis to research the existential problem of price series. By using the means of time series analysis, the input-output, Markov processes an...This paper tries to utilize the methods of stochastic analysis and matrix analysis to research the existential problem of price series. By using the means of time series analysis, the input-output, Markov processes and the modern matrix analysis, the limiting problem of price balance and vibration in stochastic economic environment has been researched, and surprising conclusions obtained are as following： the probability that the economic collapse time is equal ∞ is 0.展开更多
基金Supported by CNPq-Conselho Nacional de Desenvolvimento Cient'fico e Tecnológico
文摘In this paper, we study the large time behavior of solutions of the parabolic semilinear equation δtu-div（a（x）△↓u） = -｜u｜^αu in （0,∞） × R^N, where α 〉 0 is constant and a∈ Cb^1（R^N） is a symmetric periodic matrix satisfying some ellipticity assumptions.Considering an integrable initial data u0 and α ∈ （2/N, 3/N）, we prove that the large time behavior of solutions is given by the solution U（t, x） of the homogenized linear problem δtU-div（a^h△↓U）=0,U（0） = C, where a^h is the homogenized matrix of a（x）, C is a positive constant and δ is the Dirac measure at 0.
文摘This paper tries to utilize the methods of stochastic analysis and matrix analysis to research the existential problem of price series. By using the means of time series analysis, the input-output, Markov processes and the modern matrix analysis, the limiting problem of price balance and vibration in stochastic economic environment has been researched, and surprising conclusions obtained are as following： the probability that the economic collapse time is equal ∞ is 0.
