The boundary degeneracy theory of a strongly degenerate parabolic equation
نویسندگان
چکیده
منابع مشابه
The geometric properties of a degenerate parabolic equation with periodic source term
In this paper, we discuss the geometric properties of solution and lower bound estimate of ∆um−1 of the Cauchy problem for a degenerate parabolic equation with periodic source term ut =∆um+ upsint. Our objective is to show that: (1)with continuous variation of time t, the surface ϕ = [u(x,t)]mδq is a complete Riemannian manifold floating in space RN+1and is tangent to the space RN at ∂H0(t); (2...
متن کاملBoundary Estimates for a Degenerate Parabolic Equation with Partial Dirichlet Boundary Conditions
We study the boundary regularity properties and derive pointwise a priori supremum estimates of weak solutions and their derivatives in terms of suitable weighted L-norms for a class of degenerate parabolic equations that satisfy homogeneous Dirichlet boundary conditions on certain portions of the boundary. Such equations arise in population genetics in the study of models for the evolution of ...
متن کاملThe Singular Diffusion Equation with Boundary Degeneracy
Abstract: For the heat conduction on a bounded domain with boundary degeneracy, though its diffusion coefficient vanishes on the boundary, it is still possible that the heat flux may transfer across the boundary. A known result shows that the key role is the ratio of the diffusion coefficient near the boundary. If this ratio is large enough, the heat flux transference has not any relation to th...
متن کاملBlow-Up Analysis for a Quasilinear Degenerate Parabolic Equation with Strongly Nonlinear Source
and Applied Analysis 3 Mu et al. 19 studied the secondary critical exponent for the following p-Laplacian equation with slow decay initial values: ut div ( |∇u|p−2∇u ) u, x, t ∈ R × 0, T , u x, 0 u0 x , x ∈ R, 1.6 where p > 2, q > 1, and showed that, for q > q∗ c p − 1 p/N , there exists a secondary critical exponent ac p/ q 1 − p such that the solution u x, t of 1.6 blows up in finite time for...
متن کاملOn a Semilinear Strongly Degenerate Parabolic Equation in an Unbounded Domain
We study the existence and long-time behavior of solutions to a semilinear strongly degenerate parabolic equation on R under an arbitrary polynomial growth order of the nonlinearity. To overcome some significant difficulty caused by the lack of compactness of the embeddings, the existence of global attractors is proved by combining the tail estimates method and the asymptotic a priori estimate ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Boundary Value Problems
سال: 2016
ISSN: 1687-2770
DOI: 10.1186/s13661-015-0516-0