Multidimensional Thermoelasticity for Nonsimple Materials -- Well-Posedness and Long-Time Behavior [PDF]
, 2016 An initial-boundary value problem for the multidimensional type III thermoelaticity for a nonsimple material with a center of symmetry is considered. In the linear case, the well-posedness with and without Kelvin-Voigt and/or frictional damping in the ...
Anikushyn, Andrii, Pokojovy, Michael
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On a generalized Kirchhoff equation with sublinear nonlinearities
, 2016 In this paper we consider a generalized Kirchhoff? equation in a bounded domain under the effect of a sublinear nonlinearity. Under suitable assumptions on the data of the problem we show that, with a simple change of variable, the equation can be ...
Júnior, João R. Santos +1 more
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On the approximation of $SBD$ functions and some applications [PDF]
, 2019 Three density theorems for three suitable subspaces of $SBD$ functions, in the strong $BD$ topology, are proven. The spaces are $SBD$, $SBD^p_\infty$, where the absolutely continuous part of the symmetric gradient is in $L^p$, with $p>1$, and $SBD^p ...
Crismale, Vito
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A 3-dimensional singular kernel problem in viscoelasticity: an existence result
, 2018 Materials with memory, namely those materials whose mechanical and/or thermodynamical behaviour depends on time not only via the present time, but also through its past history, are considered.
Carillo, Sandra
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A Note on a Two-Temperature Model in Linear Thermoelasticity
, 2015 We discuss the so-called two-temperature model in linear thermoelasticity and provide a Hilbert space framework for proving well-posedness of the equations under consideration.
Mukhopadhyay, Santwana +3 more
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Dynamics for wave equations connected in parallel with nonlinear localized damping
Advances in Nonlinear AnalysisThis study investigates the properties of solutions about one-dimensional wave equations connected in parallel under the effect of two nonlinear localized frictional damping mechanisms.
Gao Yunlong, Sun Chunyou, Zhang Kaibin
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On cavitation in Elastodynamics [PDF]
, 2012 Motivated by the works of Ball (1982) and Pericak-Spector and Spector (1988), we investigate singular solutions of the compressible nonlinear elastodynamics equations.
Giesselmann, Jan +1 more
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Existence results of positive solutions for Kirchhoff type equations via bifurcation methods
, 2017 In this paper we address the following Kirchhoff type problem \begin{equation*} \left\{ \begin{array}{ll} -\Delta(g(|\nabla u|_2^2) u + u^r) = a u + b u^p& \mbox{in}~\Omega, u>0& \mbox{in}~\Omega, u= 0& \mbox{on}~\partial\Omega, \end{array} \right.
Cintra, Willian +3 more
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Non-linear biphasic mixture model: Existence and uniqueness results
European Journal of Applied MathematicsThis paper is concerned with the development and analysis of a mathematical model that is motivated by interstitial hydrodynamics and tissue deformation mechanics (poro-elasto-hydrodynamics) within an in-vitro solid tumour.
Meraj Alam +2 more
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Exact determination of the volume of an inclusion in a body having constant shear modulus
, 2014 We derive an exact formula for the volume fraction of an inclusion in a body when the inclusion and the body are linearly elastic materials with the same shear modulus.
Milton, Graeme W., Thaler, Andrew E.
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