Local existence and blow up for p-Laplacian equation with logarithmic nonlinearity
نویسندگان
چکیده
منابع مشابه
Global Existence and Blow-Up Solutions and Blow-Up Estimates for Some Evolution Systems with p-Laplacian with Nonlocal Sources
This paper deals with p-Laplacian systems ut − div(|∇u|p−2∇u) = ∫ Ωv α(x, t)dx, x ∈Ω, t > 0, vt − div(|∇v|q−2∇v) = ∫ Ωu β(x, t)dx, x ∈ Ω, t > 0, with null Dirichlet boundary conditions in a smooth bounded domain Ω ⊂ RN , where p,q ≥ 2, α,β ≥ 1. We first get the nonexistence result for related elliptic systems of nonincreasing positive solutions. Secondly by using this nonexistence result, blow ...
متن کاملExistence and blow-up of solution of Cauchy problem for the sixth order damped Boussinesq equation
In this paper, we consider the existence and uniqueness of the global solution for the sixth-order damped Boussinesq equation. Moreover, the finite-time blow-up of the solution for the equation is investigated by the concavity method.
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 کاملGlobal Existence, Exponential Decay and Blow-Up of Solutions for a Class of Fractional Pseudo-Parabolic Equations with Logarithmic Nonlinearity
In this paper, we study the fractional pseudo-parabolic equations ut +(−4) u+(−4) ut = u log |u|. Firstly, we recall the relationship between the fractional Laplace operator (−4) and the fractional Sobolev space H and discuss the invariant sets and the vacuum isolating behavior of solutions with the help of a family of potential wells. Then, we derive a threshold result of existence of global w...
متن کاملBlow-up with logarithmic nonlinearities
We study the asymptotic behaviour of nonnegative solutions of the nonlinear diffusion equation in the half-line with a nonlinear boundary condition, ut = uxx − λ(u + 1) log(u + 1) (x, t) ∈ R+ × (0, T ), −ux(0, t) = (u + 1) log(u + 1)(0, t) t ∈ (0, T ), u(x, 0) = u0(x) x ∈ R+, with p, q, λ > 0. We describe in terms of p, q and λ when the solution is global in time and when it blows up in f...
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: Miskolc Mathematical Notes
سال: 2022
ISSN: ['1586-8850', '1787-2405', '1787-2413']
DOI: https://doi.org/10.18514/mmn.2022.3490