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An optimal control problem for a parabolic equation in non-cylindrical domains

Systems & Control Letters, 1988
The authors study an optimal control problem for a parabolic equation with homogeneous Dirichlet data described by \[ (1)\quad (\partial /\partial t)y(t,x)=\Delta y(t,x)+u(t,x),\quad t\geq 0,\quad x\in \Omega_ t, \] \[ y(0,x)=y_ 0(x),\quad x\in \Omega_ 0,\quad y(t,x)=0,\quad t\geq 0,\quad x\in \Gamma_ t. \] Here, \(\Omega_ t\) is a bounded open set of \
Da Prato, G., Zolésio, J. P.
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The stability and stabilization of heat equation in non-cylindrical domain

Journal of Mathematical Analysis and Applications, 2021
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Li, Lingfei, Gao, Hang
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On the dissipative Boussinesq equation in a non-cylindrical domain

Nonlinear Analysis: Theory, Methods & Applications, 2007
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Clark, H. R.   +3 more
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Discontinuous Galerkin methods for the linear Schrödinger equation in non-cylindrical domains

Numerische Mathematik, 2010
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D. C. Antonopoulou, Michael Plexousakis
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Stability of degenerate heat equation in non-cylindrical/cylindrical domain

Zeitschrift für angewandte Mathematik und Physik, 2019
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Gao, Hang, Li, Lingfei, Liu, Zhuangyi
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Beam evolution equation with variable coefficients in non‐cylindrical domains

Mathematical Methods in the Applied Sciences, 2007
AbstractIn this article, we present results concerning with the existence of global solutions and a rate decay estimate for energy associated with an initial and boundary value problem for a beam evolution equation with variable coefficients in non‐cylindrical domains. Copyright © 2007 John Wiley & Sons, Ltd.
C. S. Q. De Caldas   +2 more
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$ L_p$-solubility of the Dirichlet problem for the heat equation in non-cylindrical domains

Sbornik: Mathematics, 2002
This paper deals with the \(L^p\)-solvability of the Dirichlet problem for the heat equation in non-cylindrical domains with characteristic points at the boundary. The author studies the first boundary value problem in weighted \(L^p\)-spaces. He proposes an approach, which enables him to find a necessary and sufficient condition for the unique ...
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Properties of the Solution of a Problem for a Pseudoparabolic Equation in a Non‐Cylindrical Domain

Mathematical Methods in the Applied Sciences
ABSTRACT In this paper, we investigate a boundary value problem for a third‐order pseudoparabolic equation posed in a non‐cylindrical domain. Unlike most existing studies that are restricted to rectangular domains, our analysis focuses on a non‐cylindrical domain with respect to the time variable, which requires the development of new
Myrzagali Ospanov, Akerke Merzetkhan
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