Large time behavior of solutions to a class of doubly nonlinear parabolic equations

Hua Shui Zhan

Displaying similar documents to “Large time behavior of solutions to a class of doubly nonlinear parabolic equations”

On an over-determined problem of free boundary of a degenerate parabolic equation

Jiaqing Pan (2013)

Applications of Mathematics

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This work is concerned with the inverse problem of determining initial value of the Cauchy problem for a nonlinear diffusion process with an additional condition on free boundary. Considering the flow of water through a homogeneous isotropic rigid porous medium, we have such desire: for every given positive constants $K$ and $T_{0}$ , to decide the initial value $u_{0}$ such that the solution $u (x, t)$ satisfies ${sup}_{x \in H_{u} (T_{0})} | x | \geq K$ , where $H_{u} (T_{0}) = {x \in ℝ^{N} : u (x, T_{0}) > 0}$ . In this paper, we first establish a priori estimate $u_{t} \geq C (t) u$ and a more precise Poincaré type...

A global differentiability result for solutions of nonlinear elliptic problems with controlled growths

Luisa Fattorusso (2008)

Czechoslovak Mathematical Journal

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Let $Ω$ be a bounded open subset of $ℝ^{n}$ , $n > 2$ . In $Ω$ we deduce the global differentiability result $u \in H^{2} (Ω, ℝ^{N})$ for the solutions $u \in H^{1} (Ω, ℝ^{n})$ of the Dirichlet problem $u - g \in H_{0}^{1} (Ω, ℝ^{N}), - \sum_{i} D_{i} a^{i} (x, u, D u) = B_{0} (x, u, D u)$ with controlled growth and nonlinearity $q = 2$ . The result was obtained by first extending the interior differentiability result near the boundary and then proving the global differentiability result making use of a covering procedure.

On a class of elliptic operators with unbounded coefficients in convex domains

Giuseppe Da Prato, Alessandra Lunardi (2004)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We study the realization $A$ of the operator $A = \frac{1}{2} △ - (D U, D \cdot)$ in $L^{2} (Ω, μ)$ , where $Ω$ is a possibly unbounded convex open set in $R^{N}$ , $U$ is a convex unbounded function such that ${lim}_{x \to \partial Ω, x \in Ω} U (x) = + \infty$ and ${lim}_{|x| \to + \infty, x \in Ω} U (x) = + \infty$ , $D U (x)$ is the element with minimal norm in the subdifferential of $U$ at $x$ , and $μ (d x) = c \exp (- 2 U (x)) d x$ is a probability measure, infinitesimally invariant for $A$ . We show that $A$ , with domain $D (A) = \{u \in H^{2} (Ω, μ) : (D U, D u) \in L^{2} (Ω, μ)\}$ is a dissipative self-adjoint operator in $L^{2} (Ω, μ)$ . Note that the functions in the domain of $A$ do not satisfy any particular boundary condition. Log-Sobolev and Poincaré inequalities...