The Experts below are selected from a list of 201 Experts worldwide ranked by ideXlab platform
Kamsing Nonlaopon - One of the best experts on this subject based on the ideXlab platform.
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on the Convolution Equation related to the diamond klein gordon operator
Abstract and Applied Analysis, 2011Co-Authors: Amphon Liangprom, Kamsing NonlaoponAbstract:We study the distribution
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on the Convolution Equation related to the klein gordon operator
International journal of pure and applied mathematics, 2011Co-Authors: Amphon Liangprom, Kamsing NonlaoponAbstract:In this paper, we study the distribution ex (� + m 2 ) k �, where (� + m 2 ) k is the Klein-Gordon operator iterated k times defined by (1.14), k is a non-negative integer, � is the Dirac-delta distribution, m is a non-negative real number, x = (x1,x2,...,xn) is a variable and � = (�1,�2,...,�n) is a constant and both are the points in the n-dimensional Euclidean spaces R n . At first, the properties of ex (�+m 2 ) kare studied and after that we study the application of ex (� + m 2 ) kfor solving the solution of the Convolution Equation ex (� + m 2 ) k � � u(x) = ex M X r=0 Cr(� + m 2 ) r �, where u(x) is the generalized function and Cr is a constant. It found that the type of solutions of this Convolution Equation, such as the ordinary function and the singular distribution depend on the relationship between the values of k and M.
Sergei Trofimchuk - One of the best experts on this subject based on the ideXlab platform.
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separation dichotomy and wavefronts for a nonlinear Convolution Equation
Journal of Mathematical Analysis and Applications, 2014Co-Authors: Carlos Gomez, Humberto Prado, Sergei TrofimchukAbstract:Abstract This paper is concerned with a scalar nonlinear Convolution Equation, which appears naturally in the theory of traveling waves for monostable evolution models. First, we prove that, at each end of the real line, every bounded positive solution of the Convolution Equation should either be separated from zero or be exponentially converging to zero. This dichotomy principle is then used to establish a general theorem guaranteeing the uniform persistence and existence of semi-wavefront solutions to the Convolution Equation. Finally, we apply our theoretical results to several well-studied classes of evolution Equations with asymmetric non-local and non-monotone response. We show that, contrary to the symmetric case, these Equations can possess simultaneously stationary, expansion and extinction waves.
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on uniqueness of semi wavefronts diekmann kaper theory of a nonlinear Convolution Equation re visited
arXiv: Classical Analysis and ODEs, 2010Co-Authors: Maitere Aguerrea, Carlos Gomez, Sergei TrofimchukAbstract:Motivated by the uniqueness problem for monostable semi-wavefronts, we propose a revised version of the Diekmann and Kaper theory of a nonlinear Convolution Equation. Our version of the Diekmann-Kaper theory allows 1) to consider new types of models which include nonlocal KPP type Equations (with either symmetric or anisotropic dispersal), non-local lattice Equations and delayed reaction-diffusion Equations; 2) to incorporate the critical case (which corresponds to the slowest wavefronts) into the consideration; 3) to weaken or to remove various restrictions on kernels and nonlinearities. The results are compared with those of Schumacher (J. Reine Angew. Math. 316: 54-70, 1980), Carr and Chmaj (Proc. Amer. Math. Soc. 132: 2433-2439, 2004), and other more recent studies.
Weibin Zeng - One of the best experts on this subject based on the ideXlab platform.
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the choquet deny Convolution Equation μ μ σ for probability measures on abelian semigroups
Journal of Theoretical Probability, 1990Co-Authors: Gabor J Szekely, Weibin ZengAbstract:In this note, we characterize the regular probability measures μ satisfying the Choquet-Deny Convolution Equation μ=μ*σ on Abelian topological semigroups for a given probability measure σ.
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The Choquet-Deny Convolution Equation μ=μ*σ for probability measures on Abelian semigroups
Journal of Theoretical Probability, 1990Co-Authors: Gabor J Szekely, Weibin ZengAbstract:In this note, we characterize the regular probability measures μ satisfying the Choquet-Deny Convolution Equation μ=μ*σ on Abelian topological semigroups for a given probability measure σ.
Amphon Liangprom - One of the best experts on this subject based on the ideXlab platform.
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on the Convolution Equation related to the diamond klein gordon operator
Abstract and Applied Analysis, 2011Co-Authors: Amphon Liangprom, Kamsing NonlaoponAbstract:We study the distribution
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on the Convolution Equation related to the klein gordon operator
International journal of pure and applied mathematics, 2011Co-Authors: Amphon Liangprom, Kamsing NonlaoponAbstract:In this paper, we study the distribution ex (� + m 2 ) k �, where (� + m 2 ) k is the Klein-Gordon operator iterated k times defined by (1.14), k is a non-negative integer, � is the Dirac-delta distribution, m is a non-negative real number, x = (x1,x2,...,xn) is a variable and � = (�1,�2,...,�n) is a constant and both are the points in the n-dimensional Euclidean spaces R n . At first, the properties of ex (�+m 2 ) kare studied and after that we study the application of ex (� + m 2 ) kfor solving the solution of the Convolution Equation ex (� + m 2 ) k � � u(x) = ex M X r=0 Cr(� + m 2 ) r �, where u(x) is the generalized function and Cr is a constant. It found that the type of solutions of this Convolution Equation, such as the ordinary function and the singular distribution depend on the relationship between the values of k and M.
Carlos Gomez - One of the best experts on this subject based on the ideXlab platform.
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separation dichotomy and wavefronts for a nonlinear Convolution Equation
Journal of Mathematical Analysis and Applications, 2014Co-Authors: Carlos Gomez, Humberto Prado, Sergei TrofimchukAbstract:Abstract This paper is concerned with a scalar nonlinear Convolution Equation, which appears naturally in the theory of traveling waves for monostable evolution models. First, we prove that, at each end of the real line, every bounded positive solution of the Convolution Equation should either be separated from zero or be exponentially converging to zero. This dichotomy principle is then used to establish a general theorem guaranteeing the uniform persistence and existence of semi-wavefront solutions to the Convolution Equation. Finally, we apply our theoretical results to several well-studied classes of evolution Equations with asymmetric non-local and non-monotone response. We show that, contrary to the symmetric case, these Equations can possess simultaneously stationary, expansion and extinction waves.
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on uniqueness of semi wavefronts diekmann kaper theory of a nonlinear Convolution Equation re visited
arXiv: Classical Analysis and ODEs, 2010Co-Authors: Maitere Aguerrea, Carlos Gomez, Sergei TrofimchukAbstract:Motivated by the uniqueness problem for monostable semi-wavefronts, we propose a revised version of the Diekmann and Kaper theory of a nonlinear Convolution Equation. Our version of the Diekmann-Kaper theory allows 1) to consider new types of models which include nonlocal KPP type Equations (with either symmetric or anisotropic dispersal), non-local lattice Equations and delayed reaction-diffusion Equations; 2) to incorporate the critical case (which corresponds to the slowest wavefronts) into the consideration; 3) to weaken or to remove various restrictions on kernels and nonlinearities. The results are compared with those of Schumacher (J. Reine Angew. Math. 316: 54-70, 1980), Carr and Chmaj (Proc. Amer. Math. Soc. 132: 2433-2439, 2004), and other more recent studies.