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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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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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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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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Exact controllability for a one-dimensional wave equation in non-cylindrical domains
Journal of Mathematical Analysis and Applications, 2013 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Cui, Lizhi, Liu, Xu, Gao, Hang
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Universal Algorithm for Simulating and Evaluating Cyclic Voltammetry at Macroporous Electrodes by Considering Random Arrays of Microelectrodes [PDF]
, 2020 An algorithm for the simulation and evaluation of cyclic voltammetry (CV) at macroporous electrodes such as felts, foams, and layered structures is presented.
Andrae, Dirk +4 more
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Weak solutions of parabolic equations in non-cylindrical domains [PDF]
Proceedings of the American Mathematical Society, 1997 In their classical work, Ladyzhenskaya and Ural ′ ’ tseva gave a definition of weak solution for parabolic equations in cylindrical domains. Their definition was broad enough to guarantee the solvability of all such problems but narrow enough to guarantee the uniqueness of these solutions.
Brown, Russell M. +2 more
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Exact Null Controllability of a One-Dimensional Wave Equation with a Mixed Boundary
Mathematics, 2023 In this paper, exact null controllability of one-dimensional wave equations in non-cylindrical domains was discussed. It is different from past papers, as we consider boundary conditions for more complex cases.
Lizhi Cui, Jing Lu
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p-Laplacian wave equations in non-cylindrical domains
, 2021 This paper is devoted to studying the stability of p-Laplacian wave equations with strong damping in non-cylindrical domains. The method of proof based on some estimates for time-varying coefficients rising from moving boundary and a modified Kormonik inequality.
Liu, Lingyang, Gao, Hang
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Case Studies in Thermal Engineering, 2022 The mutual interaction of thermal stratification and solutal stratification in mixed convection flow regimes claims many thermal engineering standpoints in daily life and so holds the interest of researchers in the thermal science of fluid flows.
Khalil Ur Rehman, Wasfi Shatanawi
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