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Saturday, August 1, 2020 | History

4 edition of A class of improper boundary value problems with damped Cauchy data. found in the catalog. # A class of improper boundary value problems with damped Cauchy data.

## by J. M. Zimmerman

Published by Courant Institute of Mathematical Sciences, New York University in New York .
Written in English

The Physical Object
Pagination25 p.
Number of Pages25
ID Numbers
Open LibraryOL17870025M

Formulation. Depending on the type of singularity in the integrand f, the Cauchy principal value is defined according to the following rules. 1) For a singularity at the finite number b: → + [∫ − + ∫ + ()] where b is a point at which the behavior of the function f is such that ∫ = ± ∞ for any a b (see plus or minus for precise usage of notations. Begehr H. () Boundary value problems for systems with Cauchy-Riemannian main part. In: Cazacu C.A., Boboc N., Jurchescu M., Suciu I. (eds) Complex Analysis — Fifth Romanian-Finnish Seminar. Lecture Notes in Mathematics, vol

In  we reduced the solution of a classical boundary-value problem, namely the biharmonic equation in a rectangular domain, to a Cauchy formulation. The . In this paper it is proved that the Cauchy problem and a boundary value problem for the Laplace equation is well-posed provided the data belong to a suitable function space. Explicit numerical procedures are described for approximating the solutions to these problems.

The initial-boundary value problem for a class of third order pseudoparabolic equations In this paper, a priori estimate for a linear third pseudoparabolic operator with bound is established, and applying the above result, the existence and uniqueness theorem of solutions for a class of nonlinear. Cauchy Problem for Generalized IMBq Equation (G-W Chen & S-B Wang) Inertial Manifolds for a Nonlocal Kuramoto–Sivashinsky Equation (J-Q Duan et al.) Weak Solutions of the Generalized Magnetic Flow Equations (S-H He & Z-D Dai) The Solution of Hammerstein Integral Equation Without Coercive Conditions (Y-L Shu).

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### A class of improper boundary value problems with damped Cauchy data by J. M. Zimmerman Download PDF EPUB FB2

In mathematics, a Cauchy (French:) boundary condition augments an ordinary differential equation or a partial differential equation with conditions that the solution must satisfy on the boundary; ideally so to ensure that a unique solution exists. A Cauchy boundary condition specifies both the function value and normal derivative on the boundary of the domain.

The basic theory for a class of initial value problems for some fractional differential equation involving Riemann-Liouville differential operators is discussed by employing the classical approach.

The main aim of Boundary Value Problems is to provide a forum to promote, encourage, and bring together various disciplines which use the theory, methods, and applications of boundary value problems. Boundary Value Problems will publish very high quality research articles on boundary value problems for ordinary, functional, difference, elliptic, parabolic, and hyperbolic differential.

The initial boundary value problem and the Cauchy problem of some generalized Boussinesq equations, were studied in   . Lie classical method has recently been applied to.

The initial-boundary value problem for a class of nonlinear higher-order wave equations system with a damping and source terms in bounded domain is studied. We prove the existence of global solutions. Cauchy principal value integrals with kernel density containing parameters.

The problem for interchange of order of integration. Inversion formulas for Cauchy principal value integrals. Cauchy-type Integrals along a Straight Line. Class. Cauchy-type integrals on the real axis and their properties. Conditions for Boundary Values of Analytic. The Cauchy problem for the damped wave equation u tt + Bu t − ∆u = f (u) + g(x), t > 0, x ∈ R N, N ≤ 3, with the initial data in X (s j) can be thus viewed in the form d dt.

Chen, Initial boundary value problem for a damped nonlinear hyperbolic equation, J. Partial Differential Equations, 16 (), Google Scholar  D. Henry, Geometric theory of semilinear parabolic equations, in Lecture Notes in Mathematics,Springer-Verlag, Berlin-New York, Google Scholar .

This paper considers the initial boundary value problem of solutions for a class of sixth order 1-D nonlinear wave equations. We discuss the probabilities of the existence and nonexistence of global solutions and give some sufficient conditions for the global and non-global existence of solutions at three different initial energy levels, i.e., sub-critical level, critical level and sup.

() Initial boundary value problem for a class of non-linear strongly damped wave equations. Mathematical Methods in the Applied Sciences() Existence and asymptotic behaviour of solutions for a class of quasi-linear evolution.

A Cauchy problem in mathematics asks for the solution of a partial differential equation that satisfies certain conditions that are given on a hypersurface in the domain. A Cauchy problem can be an initial value problem or a boundary value problem (for this case see also Cauchy boundary condition) or it can be either of is named after Augustin Louis Cauchy.

Global well-posedness and asymptotic behavior of a class of initial-boundary-value problem of the Korteweg-De Vries equation on a finite domain.

Mathematical Control & Related Fields. 25 Problems: Separation of Variables - Heat Equation 26 Problems: Eigenvalues of the Laplacian - Laplace 27 Problems: Eigenvalues of the Laplacian - Poisson 28 Problems: Eigenvalues of the Laplacian - Wave 29 Problems: Eigenvalues of the Laplacian - Heat Heat Equation with Periodic Boundary Conditions in 2D.

() Cauchy problem for a higher order generalized Boussinesq-type equation with hydrodynamical damped term. Applicable Analysis() Global existence and nonexistence of the initial–boundary value problem for the dissipative Boussinesq equation.

Y. Wang and Y. Wang, On the initial-boundary problem for fourth order wave equations with damping, strain and source terms, J. Math. Anal. Appl. (), no. 1, –  R. Xu, Initial boundary value problem for semilinear hyperbolic equations and parabolic equations with critical initial data, Quart.

Appl. Boundary Value Problems is a translation from the Russian of lectures given at Kazan and Rostov Universities, dealing with the theory of boundary value problems for analytic functions.

The emphasis of the book is on the solution of singular integral equations with Cauchy and Hilbert kernels. On the initial boundary value problem for the damped Boussinesq equation.

Discrete & Continuous Dynamical Systems - A,4 (3): doi: /dcds  Shaoyong Lai, Yong Hong Wu. The asymptotic solution of the Cauchy problem for a generalized Boussinesq equation. Bubnov, Generalized boundary value problems for the Korteweg-de Vries equation in bounded domain, Differential Equations, 15 (), Google Scholar  B.

Bubnov, Solvability in the large of nonlinear boundary-value problem for the Korteweg-de Vries equations, Differential Equations, 16 (), Google Scholar .

The Cauchy problem for an elliptic equation is a typical ill-posed problem of Mathematical Physics. The solution to the Cauchy problem for an elliptic equation is unstable with respect to small perturbations of data. For the problem to be conditionally well-posed, we should restrict the class of admissible solutions.

The problems in the first 8 chapters are suitable for an introductory course at undergraduate level and cover power series, Cauchy's theorem, Laurent series, singularities and meromorphic functions, the calculus of residues, conformal mappings, and harmonic fun.

chapter conformal mappings, boundary value problem. 7 Solutions Chapter. Hon and Wu  have determined an unknown boundary of a two-dimensional domain from Cauchy data using the radial interpolation for Hermite-Birkhoff data and the shift invariabihty of the harmonic.In this paper we study the inverse boundary value problem of determining the potential in the Schrödinger equation from the knowledge of the Dirichlet-to-Neumann map, which is commonly accepted as an ill-posed problem in the sense that, under general settings, the optimal stability estimate is of logarithmic type.

In this work, a Lipschitz-type stability is established assuming a priori that.We study the Riemann boundary value problem, for analytic functions in the class of analytic functions represented by the Cauchy-type integrals with density in the spaces with variable exponent.

We consider both the case when the coefficient is piecewise continuous and it may be of a more general nature, admitting its oscillation.

The explicit formulas for solutions in the variable exponent.