The Non-Homogeneous Wave Equation in Non-Cylindrical Domains
Trends in Computational and Applied Mathematics, 2001 We prove the existence and uniqueness of a global regular solution to the mixed problem for the nonhomogeneous wave equation in a noncylindrical domain using a hiperbolic nonsingular smooth transformation of the original problem to a nonlinear hyperbolic
N.A Lar'kin, M.H. Simões
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Variational Equations of Schroedinger-Type in Non-cylindrical Domains
Journal of Differential Equations, 2001 The boundary value problem \[ u(x, t)_t- i\sum (a_{ij}(x, t) u(x,t)_{x_i})_{x_j}- c(x,t) u(x,t)= f(x,t)\;\text{in }Q, \] \[ u(x,t)= 0\;\text{on }\Sigma,\quad u(x,0)= u_0(x)\;\text{on }Q_0, \] is investigated, where \(Q\subset \mathbb{R}^n\times (0,T)\) is an open subset (with the lateral boundary denoted by \(\Sigma\)) whose sections \(Q_t\) (\(t ...
BERNARDI, MARCO LUIGI +2 more
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The wave equation with internal control in non-cylindrical domains
Advances in Difference Equations, 2017 In this paper, we shall be concerned with interior controllability for a one-dimensional wave equation in a domain with moving boundary. When the speed of the moving endpoint is less than a certain constant which is less than the characteristic speed, we
Lizhi Cui
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An existence result for evolution equations in non-cylindrical domains [PDF]
Nonlinear Differential Equations and Applications NoDEA, 2013 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Fabio Paronetto
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Self-Consistent Field Modeling of Bottle-Brush with Aggrecan-like Side Chain [PDF]
BiomimeticsBottle-brush polymers with aggrecan-like side chains represent a class of biomimetic macromolecules that replicate key structural and functional features of natural complexes of aggrecans with hyaluronic acid (HA) which are the major components of ...
Ivan V. Mikhailov +3 more
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Construction of a Right Inverse for the Divergence in Non-cylindrical Time Dependent Domains
Annals of PDE, 2023 AbstractWe construct a stable right inverse for the divergence operator in non-cylindrical domains in space-time. The domains are assumed to be Hölder regular in space and evolve continuously in time. The inverse operator is of Bogovskij type, meaning that it attains zero boundary values.
Olli Saari, Sebastian Schwarzacher
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Weak solutions of fractional differential equations in non cylindrical domains
Nonlinear Analysis: Real World Applications, 2017 We study a time fractional heat equation in a noncylindrical domain. The problem is one-dimensional. We prove existence of properly defined weak solutions by means of the Galerkin approximation.
A. Kubica, P. Rybka, K. Ryszewska
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On the Exact Boundary Control for the Linear Klein-Gordon Equation in Non-cylindrical Domains
Trends in Computational and Applied Mathematics, 2020 The purpose of this paper is to study an exact boundary controllability problem in noncylindrical domains for the linear Klein-Gordon equation. Here, we work near of the extension techniques presented By J.
R. S. O. Nunes
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Dynamical boundary conditions in a non-cylindrical domain for the Laplace equation [PDF]
Journal of Mathematical Analysis and Applications, 2018 This is a new version of a previous paper submitted here in Arxiv. It has substantial changes from the previous one.
Lopes, Pedro T. P., Pereira, Marcone C.
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Dissipative Boussinesq equations on non-cylindrical domains in R^n
Electronic Journal of Differential Equations, 2010 This article concerns the initial-boundary value problem for the nonlinear Boussinesq equations on time dependent domains in $mathbb{R}^n$ with $1leq n leq 4$.
Haroldo R. Clark +3 more
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