Existence’s results for parabolic problems related to fully non linear operators degenerate or singular
نویسندگان
چکیده
In this paper we prove some existence and regularity results concerning parabolic equations ut = F (x,∇u, D u) + f(x, t) with some boundary conditions, on Ω×]0, T [, where Ω is some bounded domain which possesses the exterior cone property and F is some fully nonlinear elliptic operator, singular or degenerate.
منابع مشابه
Degenerate Parabolic Initial-Boundary Value Problems*
in Hilbert space and their realizations in function spaces as initial-boundary value problems for partial differential equations which may contain degenerate or singular coefficients. The Cauchy problem consists of solving (1.1) subject to the initial condition Jdu(0) = h. We are concerned with the case where the solution is given by an analytic semigroup; it is this sense in which the Canchy p...
متن کاملA note on critical point and blow-up rates for singular and degenerate parabolic equations
In this paper, we consider singular and degenerate parabolic equations$$u_t =(x^alpha u_x)_x +u^m (x_0,t)v^{n} (x_0,t),quadv_t =(x^beta v_x)_x +u^q (x_0,t)v^{p} (x_0,t),$$ in $(0,a)times (0,T)$, subject to nullDirichlet boundary conditions, where $m,n, p,qge 0$, $alpha, betain [0,2)$ and $x_0in (0,a)$. The optimal classification of non-simultaneous and simultaneous blow-up solutions is determin...
متن کاملA MIXED PARABOLIC WITH A NON-LOCAL AND GLOBAL LINEAR CONDITIONS
Krein [1] mentioned that for each PD equation we have two extreme operators, one is the minimal in which solution and its derivatives on the boundary are zero, the other one is the maximal operator in which there is no prescribed boundary conditions. They claim it is not possible to have a related boundary value problem for an arbitrarily chosen operator in between. They have only considered lo...
متن کاملLocal Operator Methods and Time Dependent Parabolic Equations on Non-cylindrical Domains
We investigate time dependent parabolic problems of diiusion type on open subsets of R N+1 and on networks, where the domains are possibly unbounded or non-cylindrical. The coeecients are assumed to be continuous and may be singular or degenerate at the boundary. We are looking for solutions which belong locally to suitable Sobolev spaces and vanish at the boundary. The well-posedness of the ho...
متن کاملImproved Hardy-poincaré Inequalities and Sharp Carleman Estimates for Degenerate/singular Parabolic Problems
We consider the following class of degenerate/singular parabolic operators: Pu = ut − (xux)x − λ xβ u, x ∈ (0, 1), associated to homogeneous boundary conditions of Dirichlet and/or Neumann type. Under optimal conditions on the parameters α ≥ 0, β, λ ∈ R, we derive sharp global Carleman estimates. As an application, we deduce observability and null controllability results for the corresponding e...
متن کامل