EXISTENCE OF SOLUTIONS TO A PARABOLIC p(x)-LAPLACE EQUATION WITH CONVECTION TERM VIA L∞ ESTIMATES
نویسندگان
چکیده
This article is devoted to the study of the existence of weak solutions to an initial and boundary value problem for a parabolic p(x)-Laplace equation with convection term. Using the De Giorgi iteration technique, the authors establish the critical a priori L∞-estimates and thus prove the existence of weak solutions.
منابع مشابه
Decay estimates of solutions to the IBq equation
In this paper we focus on the Cauchy problem for the generalized IBq equation with damped term in $n$-dimensional space. We establish the global existence and decay estimates of solution with $L^q(1leq qleq 2)$ initial value, provided that the initial value is suitably small. Moreover, we also show that the solution is asymptotic to the solution $u_L$ to the corresponding linear equa...
متن کاملPeriodic Solutions of p-Laplacian Systems with a Nonlinear Convection Term
((u1(x, t+ ω), (u2(x, t+ ω)) = (u1(x, t), u2(x, t)) in Q, where △pu = div(|∇u| p−2 ∇u) is the so-called p−Laplacian operator, Ω is a bounded convex subset in R , Q := Ω × (0, ω), S := ∂Ω × (0, ω), ∂Ω is the boundary of Ω and ω > 0. Precise conditions on ai, fi and hi will be given later. The system of form (S) is a class of degenerate parabolic systems and appears in the theory of non-Newtonian...
متن کاملBlow-up for the 1d Nonlinear Schrödinger Equation with Point Nonlinearity Ii: Supercritical Blow-up Profiles
We consider the 1D nonlinear Schrödinger equation (NLS) with focusing point nonlinearity, (0.1) i∂tψ + ∂ 2 xψ + δ|ψ|p−1ψ = 0, where δ = δ(x) is the delta function supported at the origin. In the L supercritical setting p > 3, we construct self-similar blow-up solutions belonging to the energy space Lx ∩Ḣ x. This is reduced to finding outgoing solutions of a certain stationary profile equation. ...
متن کاملFinite Volume Schemes for Nonlinear Parabolic Problems: Another Regularization Method
Abstract. On one hand, the existence of a solution to degenerate parabolic equations, without a nonlinear convection term, can be proven using the results of Alt and Luckhaus, Minty and Kolmogorov. On the other hand, the proof of uniqueness of an entropy weak solution to a nonlinear scalar hyperbolic equation, first provided by Krushkov, has been extended in two directions: Carrillo has handled...
متن کاملThe 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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2013