scholarly journals Singular Perturbations for a Class of Degenerate Parabolic Equations with Mixed Dirichlet-Neumann Boundary Conditions

2003 ◽  
Vol 10 (2) ◽  
pp. 269-296 ◽  
Author(s):  
Marie-Josée Jasor ◽  
Laurent Lévi
Keyword(s):  
Boundary Conditions ◽  
Singular Perturbations ◽  
Parabolic Equations ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Degenerate Parabolic Equations ◽  
Degenerate Parabolic

scholarly journals Stability properties of Radon measure-valued solutions for a class of nonlinear parabolic equations under Neumann boundary conditions

2021 ◽  
Vol 6 (11) ◽  
pp. 12182-12224
Author(s):  
Quincy Stévène Nkombo ◽  
◽  
Fengquan Li ◽  
Christian Tathy ◽  
Keyword(s):  
Boundary Conditions ◽  
Parabolic Equations ◽  
Radon Measure ◽  
Neumann Boundary ◽  
Large Time Behavior ◽  
Neumann Boundary Conditions ◽  
Degenerate Parabolic Equations ◽  
Measure Data ◽  
Normal Vector ◽  
Time Behavior

<abstract><p>In this paper, we address the existence, uniqueness, decay estimates, and the large-time behavior of the Radon measure-valued solutions for a class of nonlinear strongly degenerate parabolic equations involving a source term under Neumann boundary conditions with bounded Radon measure as initial data.</p> <p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{equation*} \begin{cases} u_{t} = \Delta\psi(u)+h(t)f(x, t) \ \ &amp;\text{in} \ \ \Omega\times(0, T), \\ \frac{\partial\psi(u)}{\partial\eta} = g(u) \ \ &amp;\text{on} \ \ \partial\Omega\times(0, T), \\ u(x, 0) = u_{0}(x) \ \ &amp;\text{in} \ \ \Omega, \end{cases} \end{equation*} $\end{document} </tex-math></disp-formula></p> <p>where $ T &gt; 0 $, $ \Omega\subset \mathbb{R}^{N}(N\geq2) $ is an open bounded domain with smooth boundary $ \partial\Omega $, $ \eta $ is an outward normal vector on $ \partial\Omega $. The initial value data $ u_{0} $ is a nonnegative bounded Radon measure on $ \Omega $, the function $ f $ is a solution of the linear inhomogeneous heat equation under Neumann boundary conditions with measure data, and the functions $ \psi $, $ g $ and $ h $ satisfy the suitable assumptions.</p></abstract>

Inverse problems for parabolic equations with interior degeneracy and Neumann boundary conditions

2016 ◽  
Vol 24 (3) ◽  
Author(s):  
Idriss Boutaayamou ◽  
Genni Fragnelli ◽  
Lahcen Maniar
Keyword(s):  
Boundary Conditions ◽  
Parabolic Equations ◽  
Parabolic Problem ◽  
Neumann Boundary ◽  
Spatial Domain ◽  
Neumann Boundary Conditions ◽  
Well Posedness ◽  
Degeneracy Point ◽  
Inverse Source Problems ◽  
Interior Degeneracy

AbstractWe consider a parabolic problem with degeneracy in the interior of the spatial domain and we focus on the well-posedness of the problem and on inverse source problems. The novelties of the present paper are two. First, the degeneracy point is in the interior of the spatial domain. Second, we consider Neumann boundary conditions so that no previous result can be adapted to this situation.

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