Results 301 to 310 of about 181,693 (317)
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2003
In this Chapter we study some pilot models of parabolic variational and hemivariational inequalities. The Chapter is primarily based on the works of Brezis [29], Goeleven and Motreanu [79], [91], Miettinen [125] and Quittner [156].
D. Motreanu, D. Goeleven
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In this Chapter we study some pilot models of parabolic variational and hemivariational inequalities. The Chapter is primarily based on the works of Brezis [29], Goeleven and Motreanu [79], [91], Miettinen [125] and Quittner [156].
D. Motreanu, D. Goeleven
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Applications to parabolic problems
2012In this chapter we consider the asymptotic dynamics of parabolic problems of the form $$\begin{array}{rcl}{ u}_{t} -\mbox{ div}(a(x)\nabla u) + c(x)u& =& f(x,t,u),\quad \mbox{ in}\quad \Omega, \\ u& =& 0,\quad \mbox{ on}\quad \partial \Omega, \end{array}$$ (12.1) where N is a positive integer, \(\Omega \subset {\mathbb{R}}^{N}\) is a bounded ...
Alexandre N. Carvalho +2 more
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Estimates for Parabolic Problems
2019We present quantitative estimates for the homogenization of the parabolic equation $$\begin{aligned} \partial _t u - \nabla \cdot \mathbf {a}(x) \nabla u = 0 \quad \text{ in } \ I\times U \subseteq \mathbb {R}\times {\mathbb {R}^d}. \end{aligned}$$ The coefficients \(\mathbf {a}(x)\) are assumed to depend only on the spatial variable x rather ...
Scott N. Armstrong +2 more
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Transients — parabolic problems
1972(Linear and non-linear situations. Possible use to find steady state solution. Dynamic relaxation).
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2019
Let \((V,H, V^*)\) be a Hilbert triple, with V separable and \(V\Subset H\) (cf. Chap. 17 ff.), and let \(A:V\rightarrow V^*\) be an elliptic operator associated to a continuous and coercive symmetric bilinear form on V (which can be assumed to be equal to the scalar product of V).
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Let \((V,H, V^*)\) be a Hilbert triple, with V separable and \(V\Subset H\) (cf. Chap. 17 ff.), and let \(A:V\rightarrow V^*\) be an elliptic operator associated to a continuous and coercive symmetric bilinear form on V (which can be assumed to be equal to the scalar product of V).
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2000
Let Ω be a Lipschitz bounded open subset of ℝ n with boundary Г. Denote by Г D some measurable subset of Г (for the measure dσ(x)) and by Г N the complement of Г D in Г — that is to say $$ {\Gamma_N} = \Omega \backslash {\Gamma_D} $$ (12.1) .
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Let Ω be a Lipschitz bounded open subset of ℝ n with boundary Г. Denote by Г D some measurable subset of Г (for the measure dσ(x)) and by Г N the complement of Г D in Г — that is to say $$ {\Gamma_N} = \Omega \backslash {\Gamma_D} $$ (12.1) .
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Inverse Problems for Parabolic Equations
2017This Chapter deals with inverse coefficient problems for linear second-order 1D parabolic equations. We establish, first, a relationship between solutions of direct problems for parabolic and hyperbolic equations.
Vladimir G. Romanov +1 more
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2004
In this chapter, we first recall the classical existence and uniqueness results for parabolic systems. We then look for uniform estimates, independent of the viscosity, in spaces with tangential or conormal smoothness.
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In this chapter, we first recall the classical existence and uniqueness results for parabolic systems. We then look for uniform estimates, independent of the viscosity, in spaces with tangential or conormal smoothness.
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2015
The main goal of this chapter is to show how the general methods developed in the previous chapters can be applied in the study of properties of qualitative dynamics for a class of abstract evolution equations of the ...
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The main goal of this chapter is to show how the general methods developed in the previous chapters can be applied in the study of properties of qualitative dynamics for a class of abstract evolution equations of the ...
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Nonlinear Analysis: Theory, Methods & Applications, 1997
Abdullah Shidfar, Hossein Azary
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Abdullah Shidfar, Hossein Azary
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