scholarly journals A note on the spatial behavior for the generalized Tricomi equation

2012 ◽  
Vol 25 (12) ◽  
pp. 2258-2261 ◽  
Author(s):  
R. Quintanilla
Keyword(s):  
Spatial Behavior ◽  
Tricomi Equation ◽  
Generalized Tricomi Equation

scholarly journals A nonlocal problem for a generalized Trikomi equation with a spectral parameter in the unbounded domain

2021 ◽  
pp. 17-26
Author(s):  
Р.Т. Зуннунов
Keyword(s):  
Half Plane ◽  
Spectral Parameter ◽  
Unbounded Domain ◽  
Nonlocal Problem ◽  
Existence Of A Solution ◽  
Tricomi Equation ◽  
Energy Integrals ◽  
Uniqueness Of The Solution ◽  
Upper Half Plane ◽  
Generalized Tricomi Equation

В данной статье изучена нелокальная задача для обобщенного уравнения Трикоми со спектральным параметром в неограниченной области эллиптическая часть которой является верхней полуплоскостью. Единственность решения поставленной задачи доказана методом интегралов энергии. Существование решения поставленной задачи доказана методом функций Грина и интегральных уравнений. In this article, we study a nonlocal problem for the generalized Tricomi equation with a spectral parameter in an unbounded domain, the elliptic part of which is the upper half-plane. The uniqueness of the solution to the problem posed is proved by the method of energy integrals. The existence of a solution to the problem is proved by the method of Green’s functions and integral equations.

scholarly journals Blow-up of energy solutions for the semilinear generalized Tricomi equation with nonlinear memory term

2021 ◽  
Vol 6 (10) ◽  
pp. 10907-10919
Author(s):  
Jincheng Shi ◽  
◽  
Jianye Xia ◽  
Wenjing Zhi ◽  
◽  
...  
Keyword(s):  
Relaxation Function ◽  
Blow Up ◽  
Combined Effect ◽  
Time Dependent ◽  
Memory Term ◽  
Nonlinear Memory ◽  
Tricomi Equation ◽  
Generalized Tricomi Equation

<abstract><p>In this paper, we investigate blow-up conditions for the semilinear generalized Tricomi equation with a general nonlinear memory term in $ \mathbb{R}^n $ by using suitable functionals and employing iteration procedures. Particularly, a new combined effect from the relaxation function and the time-dependent coefficient is found.</p></abstract>

scholarly journals A boundary value problem with a displacement for the generalized equation of Trikomi with a spectral parameter in an unbounded domain

2020 ◽  
pp. 55-64
Author(s):  
Р.Т. Зуннунов ◽  
И.У. Хайдаров
Keyword(s):  
Boundary Value Problem ◽  
Spectral Parameter ◽  
Unbounded Domain ◽  
Generalized Equation ◽  
Horizontal Strip ◽  
Method Of Integral Equations ◽  
Tricomi Equation ◽  
Energy Integrals ◽  
Uniqueness Of The Solution ◽  
Generalized Tricomi Equation

В данной работе для обобщенного уравнения Трикоми со спектральным параметром в неограниченной области эллиптическая часть которой является горизонтальной полосой исследуется задача со смещением на характеристиках разных семейств. Единственность решения задачи доказывается методом интегралов энергии, а существование решения задачи методом функций Грина и методом интегральных уравнений. In this paper, for the generalized Tricomi equation with a spectral parameter in an unbounded domain, the elliptical part of which is a horizontal strip, we study a problem with a shift on the characteristics of different families. The uniqueness of the solution to the problem is proved by the method of energy integrals, and the existence of the solution to the problem by the method of Green’s functions and the method of integral equations

scholarly journals Nonexistence result for the generalized Tricomi equation with the scale-invariant damping, mass term and time derivative nonlinearity

2021 ◽  
pp. 1-21
Author(s):  
Moahmed Fahmi Ben Hassen ◽  
Makram Hamouda ◽  
Mohamed Ali Hamza ◽  
Hanen Khaled Teka
Keyword(s):  
Blow Up ◽  
Time Derivative ◽  
Mass Term ◽  
Scale Invariant ◽  
Small Initial Data ◽  
Damping Coefficients ◽  
Nonexistence Result ◽  
Tricomi Equation ◽  
Speed Of Propagation ◽  
Generalized Tricomi Equation

In this article, we consider the damped wave equation in the scale-invariant case with time-dependent speed of propagation, mass term and time derivative nonlinearity. More precisely, we study the blow-up of the solutions to the following equation: ( E ) u t t − t 2 m Δ u + μ t u t + ν 2 t 2 u = | u t | p , in  R N × [ 1 , ∞ ) , that we associate with small initial data. Assuming some assumptions on the mass and damping coefficients, ν and μ > 0, respectively, we prove that blow-up region and the lifespan bound of the solution of ( E ) remain the same as the ones obtained for the case without mass, i.e. ( E ) with ν = 0 which constitutes itself a shift of the dimension N by μ 1 + m compared to the problem without damping and mass. Finally, we think that the new bound for p is a serious candidate to the critical exponent which characterizes the threshold between the blow-up and the global existence regions.

scholarly journals Nonexistence of Global Solutions to A Semilinear Wave Equation with Scale Invariant Damping

2021 ◽  
pp. 10-26
Author(s):  
Changwang Xiao
Keyword(s):  
Wave Equation ◽  
Critical Case ◽  
Global Solutions ◽  
Fundamental Solutions ◽  
Scale Invariant ◽  
Semilinear Wave Equation ◽  
Change Of Variables ◽  
Tricomi Equation ◽  
Blowup Result ◽  
Generalized Tricomi Equation

We obtain a blowup result for solutions to a semilinear wave equation with scale-invariant dissipation. We perform a change of variables that transforms our starting equation into a Generalized Tricomi equation, then apply Kato’s lemma, we can prove a blowup result for solutions to the transformed equation under some assumptions on the initial data. In the critical case, we use the fundamental solutions of the Generalized Tricomi equation to modify Kato’s lemma to deal with it.

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