[PDF] Top 20 Filtering Function Method for the Cauchy Problem of a Semi Linear Elliptic Equation

... given Cauchy data may result in a dramatic error on the solution ...the Cauchy problem of the homogeneous elliptic ...homogeneous problem, there have many regularization methods to deal ... See full document

... This problem appears in many applications [1] such as in Debye–Huckel theory, im- plicit marching strategies of the heat equation, the linearization of the Poisson–Boltzmann equation [2–4], and so ... See full document

... In the present paper, we give a Banach space solution theory for Equation () subject to appropriate initial conditions. Our approach is solely based on the step method and does not incorporate any ... See full document

... p-Laplacian equation, as an important class of parabolic equations, comes from the compressible fluid flows in a homogeneous isotropic rigid porous ...classical linear heat equation, this ... See full document

... our problem can be reduced to the study of an abstract differential equation associated to some nonlocal boundary conditions involving a linear un- bounded ...our problem can be transformed by ... See full document

... E , while A t     , B t , and C t   are families of linear or nonlinear differential type operators acting in E , some of which become zero or infinite at t  0 . They considered appropriate initial data u  ... See full document

... the linear problem, we restrict the main result for the semilinear part to the case when Σ = ...with linear equations and requires a Maximum Principle’s Theorem in order to prove that the ... See full document

... of problem is, the different type of nonlinear differential equation can only be efficiently solved by different corresponding ...Jacobi elliptic function expan- sion method [7], the ... See full document

... The nonlocal Cauchy problem for semi linear evolution for partial neutral functional differential equations with equations in Banach space was studied first by Byszekswi [7, nonlocal con[r] ... See full document

... homogeneous problem (f ≡ ) was studied with various methods in many ...element method, the homogeneous problems were considered in [, , ] ...the Cauchy problem for a linear ... See full document

... [2] A. B. Aliev and B. H. Lichaei, “Existence and Non-Exis- tence of Global Solutions of the Cauchy Problem for High- er Semi-Linear Pseudo-Hyperbolic Equations,” Nonlinear Analysis, Theory, ... See full document

... ill-posed Cauchy problem in a half-plane. This problem is novel since the Cauchy data on the accessible boundary is given, whilst the additional temperature is involved on a ...redefined ... See full document

... fitness function. The algorithm is based on function evalua- tions which are implemented by repeatedly solving the state Equations ...of function evaluations we reached the result of optimization ... See full document

... In this work the reconstruction of lacking boundary data on a part of the boundary of a body from partially-overspecified boundary conditions on another part has been investigated numerically. A domain decomposition like ... See full document

... in Equation (1), then the resulted equation is the Schrödinger ...Schrödinger equation, the well-posedness problem is investigated for various nonlinear terms f ...the problem (1) can ... See full document

... conduction problem is ...squares method and the error estimate of logarithmic Hölder type between the approximate solution and the exact ones by choosing a suitable regularization ... See full document

... the Cauchy problem for a model of nonlinear dissipative evolution ...The linear part is a pseudodifferential operator and the nonlinearity is a cubic pseudodifferential operator defined by means of the ... See full document

... nonlinear function, which is optimal in the sense of the least-squares among all polynomial expansions at the working point; Gram-Charlie expansions of probability densities have been employed for state ... See full document

... Many physical phenomena have been formulated as a mathematical model with nonlocal boundary conditions. A short overview of these models is presented in many papers (see, for example, works [1, 2]). Particulary, many ... See full document

... tion, Quart. Appl. Math. 53 (1995), no. 2, 245–258. MR 96b:45002. Zbl 823.65145. [7] A. Gerasoulis, The use of piecewise quadratic polynomials for the solution of singular integral equations of Cauchy type, ... See full document