We consider a class of diffusion equations with the Caputo time-fractionalderivative partial derivative(alpha)(t)u=Lu subject to the homogeneous Dirichlet boundary ***, we consider a fractional order 0<alpha<1 a...
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We consider a class of diffusion equations with the Caputo time-fractionalderivative partial derivative(alpha)(t)u=Lu subject to the homogeneous Dirichlet boundary ***, we consider a fractional order 0logarithmicconvexity extends to this non-symmetric case provided that the drift coefficientis given by a gradient vector field. Next, we perform some numerical experiments to validate the theoretical results in both symmetric and non-symmetric ***, some conclusions and open problems will be mentioned.
In this short note, we want to describe the logarithmic convexity argument for third order in time partial differential equations. As a consequence, we first prove a uniqueness result whenever certain conditions on th...
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In this short note, we want to describe the logarithmic convexity argument for third order in time partial differential equations. As a consequence, we first prove a uniqueness result whenever certain conditions on the parameters are satisfied. Later, we show the instability of the solutions if the initial energy is less or equal than zero.
In this paper, we prove a logarithmic convexity that reflects an observability estimate at a single point of time for the one-dimensional heat equation with dynamic boundary conditions. Consequently, we establish the ...
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In this paper, we prove a logarithmic convexity that reflects an observability estimate at a single point of time for the one-dimensional heat equation with dynamic boundary conditions. Consequently, we establish the impulse approximate controllability for the impulsive heat equation with dynamic boundary conditions. Moreover, we obtain an explicit upper bound of the cost of impulse control. At the end, we give a constructive algorithm for computing the impulsive control of minimal L-2-norm. We also present some numerical tests to validate the theoretical results and show the efficiency of the designed algorithm.
In the paper, with the aid of the Cebysev integral inequality, by virtue of the integral representation of the Riemann zeta function, with the use of two properties of a function and its derivatives involving the expo...
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In the paper, with the aid of the Cebysev integral inequality, by virtue of the integral representation of the Riemann zeta function, with the use of two properties of a function and its derivatives involving the exponential function and the Stirling numbers of the second kind, by means of complete monotonicity, the authors establish logarithmic convexity and increasing property of four sequences involving the Bernoulli numbers and their ratios.
作者：
Carasso, ASNIST
Dept Math & Computat Sci Gaithersburg MD 20899 USA
This paper examines a wide class of ill-posed initial value problems for partial differential equations, and surveys logarithmic convexity results leading to Holder-continuous dependence on data for solutions satisfyi...
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This paper examines a wide class of ill-posed initial value problems for partial differential equations, and surveys logarithmic convexity results leading to Holder-continuous dependence on data for solutions satisfying prescribed bounds. The discussion includes analytic continuation in the unit disc, time-reversed parabolic equations in L-p spaces, the time-reversed Navier-Stokes equations, as well as a large class of nonlocal evolution equations that can be obtained by randomizing the time variable in abstract Cauchy problems. It is shown that in many cases, the resulting Holder-continuity is too weak to permit useful continuation from imperfect data. However, considerable reduction in the growth of errors occurs, and continuation becomes feasible, for solutions satisfying the slow evolution from the continuation boundary constraint, previously introduced by the author.
Abstract: logarithmic convexity type continuous dependence results for discrete harmonic functions defined as solutions of the standard ${C^0}$ piecewise-linear approximation to Laplace’s equation are proved....
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Abstract: logarithmic convexity type continuous dependence results for discrete harmonic functions defined as solutions of the standard ${C^0}$ piecewise-linear approximation to Laplace’s equation are proved. Using this result, error estimates for a regularization method for approximating the Cauchy problem for Poisson’s equation on a rectangle are obtained. Numerical results are presented.
In this article, the logarithmic convexity of the one-parameter mean values J(r) and the monotonicity of the product J(r)J(-r) with r is an element of R are presented. Some more general results are established.
In this article, the logarithmic convexity of the one-parameter mean values J(r) and the monotonicity of the product J(r)J(-r) with r is an element of R are presented. Some more general results are established.
For 0 < p < infinity and -2 <= alpha <= 0 we show that the L-p integral mean on rD of an analytic function in the unit disk D with respect to the weighted area measure (1 - vertical bar z vertical bar(2))(...
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For 0 < p < infinity and -2 <= alpha <= 0 we show that the L-p integral mean on rD of an analytic function in the unit disk D with respect to the weighted area measure (1 - vertical bar z vertical bar(2))(alpha) dA(z) is a logarithmically convex function of r on (0, 1).
In this article, the logarithmic convexity of the extended mean values are proved and an inequality of mean values is presented. As by-products, two analytic inequalities are derived. Two open problems are proposed.
In this article, the logarithmic convexity of the extended mean values are proved and an inequality of mean values is presented. As by-products, two analytic inequalities are derived. Two open problems are proposed.
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