Blow up and Decay for a Class of $p$-Laplacian Hyperbolic Equation with Logarithmic Nonlinearity
نویسندگان
چکیده
In this paper, we study an initial boundary value problem for a $p$-Laplacian hyperbolic equation with logarithmic nonlinearity. By combining the modified potential well method Galerkin method, existence of global weak solution is studied, and polynomial exponential decay estimation under certain conditions are also given. Moreover, by using concavity other techniques, obtain blow up results at finite time.
منابع مشابه
Global 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 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 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 کاملConvergence and Blow-up of Solutions for a Complex-valued Heat Equation with a Quadratic Nonlinearity
This paper is concerned with the Cauchy problem for a system of parabolic equations which is derived from a complex-valued equation with a quadratic nonlinearity. First we show that if the convex hull of the image of initial data does not intersect the positive real axis, then the solution exists globally in time and converges to the trivial steady state. Next, on the onedimensional space, we p...
متن کاملGlobal 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 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: Taiwanese Journal of Mathematics
سال: 2022
ISSN: ['1027-5487', '2224-6851']
DOI: https://doi.org/10.11650/tjm/220107