Results 51 to 60 of about 3,933 (187)
Journal of Applied Mathematics, Volume 2025, Issue 1, 2025.We investigate the initial value problem associated to the higher order nonlinear Schrödinger equation i∂tu+−1j+1∂x2ju=u2ju x,t≠0∈ℝ,ux,0=u0x, where j ≥ 2 is any integer, u is a complex valued function, and the initial data u0 is real analytic on ℝ and has a uniform radius of spatial analyticity σ0 in the space variable.
Tegegne Getachew +3 more
wiley +1 more source
Feedback stabilization of semilinear heat equations
Abstract and Applied Analysis, Volume 2003, Issue 12, Page 697-714, 2003., 2003 This paper is concerned with the internal and boundary stabilization of the steady‐state solutions to quasilinear heat equations via internal linear feedback controllers provided by an LQ control problem associated with the linearized equation.
V. Barbu, G. Wang
wiley +1 more source
Advances in Nonlinear Analysis, 2022 We investigate optimal decay rates for higher–order spatial derivatives of strong solutions to the 3D Cauchy problem of the compressible viscous quantum magnetohydrodynamic model in the H5 × H4 × H4 framework, and the main novelty of this work is three ...
Wang Juan, Zhang Yinghui
doaj +1 more source
A remark on reaction-diffusion equations in unbounded domains
, 2002 We prove the existence of a compact L^2-H^1 attractor for a reaction-diffusion equation in R^n. This improves a previous result of B. Wang concerning the existence of a compact L^2-L^2 attractor for the same equation.Comment: 6 pages; to appear on "Discr.
Prizzi, Martino
core +2 more sources
Journal of Mathematics, Volume 2025, Issue 1, 2025.A fourth‐order p(x)‐biharmonic‐type hyperbolic equation with variable‐exponent nonlinearities is considered. The global existence of solutions has been obtained by potential well theory and the continuous principle. Qualitative properties related to the stability of the solution of this equation are obtained using the method of the well‐known Komornik ...
Billel Gheraibia +4 more
wiley +1 more source
Existence and nonexistence of entire solutions to the logistic differential equation
Abstract and Applied Analysis, Volume 2003, Issue 17, Page 995-1003, 2003., 2003 We consider the one‐dimensional logistic problem (rαA(|u′|)u′) ′=rαp(r)f(u) on (0, ∞), u(0) > 0, u′(0) = 0, where α is a positive constant and A is a continuous function such that the mapping tA(|t|) is increasing on (0, ∞). The framework includes the case where f and p are continuous and positive on (0, ∞), f(0) = 0, and f is nondecreasing.
Marius Ghergu, Vicenţiu Rădulescu
wiley +1 more source
Global Solutions and Asymptotic Study to a 3D‐Lagrangian Boussinesq System
Journal of Mathematics, Volume 2025, Issue 1, 2025.We prove that the Lagrangian‐averaged 3D periodic Boussinesq system has a global in time weak solution that depends continuously on time. Also, we establish that a unique strong global in time solution exists. Moreover, we show that the system has a compact global attractor which is connected.
Ridha Selmi +2 more
wiley +1 more source
Generalized Cahn‐Hilliard equations based on a microforce balance
Journal of Applied Mathematics, Volume 2003, Issue 4, Page 165-185, 2003., 2003 We present some models of Cahn‐Hilliard equations based on a microforce balance proposed by M. Gurtin. We then study the existence and uniqueness of solutions.
Alain Miranville
wiley +1 more source
Self-Similar Blowup Solutions to the 2-Component Degasperis-Procesi Shallow Water System
, 2010 In this article, we study the self-similar solutions of the 2-component Degasperis-Procesi water system:% [c]{c}% \rho_{t}+k_{2}u\rho_{x}+(k_{1}+k_{2})\rho u_{x}=0 u_{t}-u_{xxt}+4uu_{x}-3u_{x}u_{xx}-uu_{xxx}+k_{3}\rho\rho_{x}=0. By the separation method,
Camassa +19 more
core +1 more source
Global Solution and Asymptotic Behaviour for a Wave Equation type p-Laplacian with Memory
Open Journal of Mathematical Analysis, 2018 In this work we study the global solution, uniqueness and asymptotic behaviour of the nonlinear equation utt − ∆pu = ∆u− g ∗ ∆u where ∆pu is the nonlinear p-Laplacian operator, p ≥ 2 and g ∗ ∆u is a memory damping.
C. Raposo, A. Cattai, J. Ribeiro
semanticscholar +1 more source