scholarly journals Large Time Behavior of Solutions to Parabolic Equations with Dirichlet Operators and Nonlinear Dependence on Measure Data

2018 ◽  
Author(s):  
Tomasz Klimsiak ◽  
Andrzej Rozkosz
Keyword(s):  
Parabolic Equations ◽  
Large Time ◽  
Large Time Behavior ◽  
Nonlinear Dependence ◽  
Measure Data ◽  
Time Behavior ◽  
Dirichlet Operators

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>

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