Initial boundary value problems for second order parabolic systems in cylinders with polyhedral base

Luong, Vu Trong; Loi, Do Van

doi:10.1186/1687-2770-2011-56

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Cited by 3 publications

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“…We can find in [7], a study of secondorder parabolic problems in both cases of finite cylinders and infinite cylinders whose bases are polyhedral domains. The functional framework dealt with by the author is different from that used in our study.…”

Section: Introductionmentioning

confidence: 99%

On Parabolic Equations with Mixed Dirichlet–Robin Type Boundary Conditions in a Non-rectangular Domain

Kheloufı

2015

Mediterr. J. Math.

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Section: Introductionmentioning

confidence: 99%

On Parabolic Equations with Mixed Dirichlet–Robin Type Boundary Conditions in a Non-rectangular Domain

Kheloufı

2015

Mediterr. J. Math.

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On the asymptotic of solution to the Dirichlet problem for hyperbolic equations in cylinders with edges

Luong¹,

Thi²

2014

Electron. J. Qual. Theory Differ. Equ.

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On some boundary value problems for the heat equation in a non-regular type of a prism of ℝ^N+1

Kheloufı

2017

Georgian Mathematical Journal

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This paper is devoted to the analysis of the boundary value problem {\partial_{t}u-\Delta u=f}, with an N-dimensional space variable, subject to a Dirichlet–Robin type boundary condition on the lateral boundary of the domain. The problem is settled in a noncylindrical domain of the form Q=\{(t,x_{1})\in\mathbb{R}^{2}:0<t<T,\varphi_{1}(t)<x_{1}<\varphi_{2}(t)\}% \times\prod_{i=1}^{N-1}{]0,b_{i}[}, where {\varphi_{1}} and {\varphi_{2}} are smooth functions. One of the main issues of the paper is that the domain can possibly be non-regular; for instance, the significant case when {\varphi_{1}(0)=\varphi_{2}(0)} is allowed. We prove well-posedness results for the problem in a number of different settings and under natural assumptions on the coefficients and on the geometrical properties of the domain. This work is an extension of the one-dimensional case studied in [4].

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Initial boundary value problems for second order parabolic systems in cylinders with polyhedral base

Abstract: The purpose of this article is to establish the well posedness and the regularity of the solution of the initial boundary value problem with Dirichlet boundary conditions for second-order parabolic systems in cylinders with polyhedral base.

Cited by 3 publications

References 8 publications

On Parabolic Equations with Mixed Dirichlet–Robin Type Boundary Conditions in a Non-rectangular Domain

On Parabolic Equations with Mixed Dirichlet–Robin Type Boundary Conditions in a Non-rectangular Domain

On the asymptotic of solution to the Dirichlet problem for hyperbolic equations in cylinders with edges

On some boundary value problems for the heat equation in a non-regular type of a prism of ℝ^N+1

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Initial boundary value problems for second order parabolic systems in cylinders with polyhedral base

Abstract: The purpose of this article is to establish the well posedness and the regularity of the solution of the initial boundary value problem with Dirichlet boundary conditions for second-order parabolic systems in cylinders with polyhedral base.

Cited by 3 publications

References 8 publications

On Parabolic Equations with Mixed Dirichlet–Robin Type Boundary Conditions in a Non-rectangular Domain

On Parabolic Equations with Mixed Dirichlet–Robin Type Boundary Conditions in a Non-rectangular Domain

On the asymptotic of solution to the Dirichlet problem for hyperbolic equations in cylinders with edges

On some boundary value problems for the heat equation in a non-regular type of a prism of ℝ N+1

Contact Info

Product

Resources

About

On some boundary value problems for the heat equation in a non-regular type of a prism of ℝ^N+1