Coefficients In Unbounded Domains Research Articles

Dirichlet problem for elliptic equations with coefficients in locally Morrey spaces

We consider the Dirichlet boundary value problem for a linear elliptic operator with discontinuous coefficients in unbounded domains. We prove the existence and uniqueness of solution in weighted Sobolev spaces.

Noncoercive nonlinear Dirichlet problems in unbounded domains

In this paper we study noncoercive nonlinear Dirichlet problems with discontinuous coefficients in unbounded domains. An existence result is proved exploiting suitable coercive nonlinear approximate Dirichlet problems.

Existence and uniqueness results in weighted spaces for Dirichlet problem in unbounded domains

We study the Dirichlet problem for a second order linear elliptic partial differential equation with discontinuous coefficients in unbounded domains. We establish an existence and uniqueness result.

Noncoercive elliptic equations with discontinuous coefficients in unbounded domains

In this paper we study Dirichlet problems for noncoercive linear elliptic equations with discontinuous coefficients in unbounded domains. Exploiting a nonlinear approach, we achieve existence, uniqueness and regularity results.

Lp -theory of boundary integral operators for domains with unbounded smooth boundary

Abstract The paper is devoted to the L p ${L^{p}}$ -theory of boundary integral operators for boundary value problems described by anisotropic Helmholtz operators with variable coefficients in unbounded domains with unbounded smooth boundary. We prove the invertibility of boundary integral operators for Dirichlet and Neumann problems in the Bessel-potential spaces H s , p ⁢ ( ∂ ⁡ D ) ${H^{s,p}(\partial D)}$ , p ∈ ( 1 , ∞ ) ${p\in(1,\infty)}$ , and the Besov spaces B p , q s ⁢ ( ∂ ⁡ D ) ${B_{p,q}^{s}(\partial D)}$ , p , q ∈ [ 1 , ∞ ] ${p,q\in[1,\infty]}$ . We prove also the Fredholmness of the Robin problem in these spaces and give the index formula.

An exponential Chebyshev second kind approximation for solving high-order ordinary differential equations in unbounded domains, with application to Dawson's integral

Abstract A new exponential Chebyshev operational matrix of derivatives based on Chebyshev polynomials of second kind (ESC) is investigated. The new operational matrix of derivatives of the ESC functions is derived and introduced for solving high-order linear ordinary differential equations with variable coefficients in unbounded domain using the collocation method. As an application the introduced method is used to evaluate Dawson's integral by solving its differential equation. The corresponding differential equation to Dawson's integral is a boundary value problem with conditions tends to infinity. The obtained numerical results are compared with the exact solution and showed good accuracy.

A new exponential Chebyshev operational matrix of derivatives for solving high-order ordinary differential equations in unbounded domains

The purpose of this paper is to investigate a new exponential Chebyshev (EC) operational matrix of derivatives. The new operational matrix of derivatives of the EC functions is derived and introduced for solving high-order linear ordinary differential equations with variable coefficients in unbounded domain using the collocation method. This method transforms the given differential equation and conditions to matrix equation with unknown EC coefficients. These matrices together with the collocation method are utilized to reduce the solution of high-order ordinary differential equations to the solution of a system of algebraic equations. The solution is obtained in terms of EC functions. Numerical examples are given to demonstrate the validity and applicability of the method. The obtained numerical results are compared with others existing methods and the exact solution where it shown to be very attractive with good accuracy.

ON THE EXPONENTIAL CHEBYSHEV APPROXIMATION IN UNBOUNDED DOMAINS: A COMPARISON STUDY FOR SOLVING HIGH-ORDER ORDINARY DIFFERENTIAL EQUATIONS

In this paper we investigate an improved scheme for exponential Chebyshev (EC) collocation method. The improved scheme of the EC func- tions is derived and introduced for solving high-order linear ordinary differential equations with variable coefficients in unbounded domain. This technique trans- forms the given differential equation and mixed conditions to matrix equation with unknown EC coefficients. These matrices together with the collocation method are utilized to reduce the solution of higher-order ordinary differential equations to the solution of a system of algebraic equations. The solution is ob- tained in terms of EC functions. Numerical examples are given to demonstrate the validity and applicability of the method. The obtained numerical results are compared with others existing methods and the exact solution where it shown to be very attractive with good accuracy.

Non autonomous parabolic problems with unbounded coefficients in unbounded domains

Given a class of nonautonomous elliptic operators $\mathcal A(t)$ with unbounded coefficients, defined in $\overline{I \times \Omega}$ (where $I$ is a right-halfline or $I=\mathbb R$ and $\Omega\subset \mathbb R^d$ is possibly unbounded), we prove existence and uniqueness of the evolution operator associated to $\mathcal A(t)$ in the space of bounded and continuous functions, under Dirichlet and first order, non tangential homogeneous boundary conditions. Some qualitative properties of the solutions, the compactness of the evolution operator and some uniform gradient estimates are then proved.

Hyperbolic Equations with Growing Coefficients in Unbounded Domains

Let Ω ⊂ ℝn, n ≥ 2, be an unbounded domain with a smooth (possibly noncompact) star-shaped boundary Γ. For the first mixed problem for a hyperbolic equation with an unbounded coefficient with power growth at infinity, the large-time behavior of the solutions is studied. Estimates for the resolvent of the spectral problem are obtained for various values of the parameters.

A priori bounds in [formula omitted] for solutions of elliptic equations in divergence form

We prove an a priori bound in Lp, p>1, for the solutions of the Dirichlet problem for second order linear elliptic partial differential equations in divergence form with discontinuous coefficients in unbounded domains.

An Lp‐Estimate for Weak Solutions of Elliptic Equations

We prove an Lp‐a priori bound, p > 2, for solutions of second order linear elliptic partial differential equations in divergence form with discontinuous coefficients in unbounded domains.

A priori inequalities for solutions of mixed boundary-value problems in unbounded domains

We prove some a priori inequalities for solutions of mixed boundary-value problems for a class of divergence form elliptic equations with discontinuous and unbounded coefficients in unbounded domains.

Dirichlet problem for a divergence form elliptic equation with unbounded coefficients in an unbounded domain

We prove existence and uniqueness of the solution of the Dirichlet problem for a class of elliptic equations in divergence form with discontinuous and unbounded coefficients in unbounded domains.

Equazioni ellittiche del secondo ordine di tipo non variazionale in aperti non limitati

In this paper we study the Dirichlet problem, for second order, linear elliptic partial differential equations with discontinuous coefficients in unbounded domains. We obtain some results about existence and uniqueness of the solution in W2(Ω).