Nonexistence of Solutions of Some Non-Linear Non-Local Evolution Systems on the Heisenberg Group

AbstractWe present non-existence results for systems of non-local in space hyperbolic equations, for systems of non-local in space parabolic equations, and for systems of non-local in space hyperbolic equations with linear damping terms. Our method of proof is based on the test function method with a help of a convexity inequality recently proved in [2].

Download Full-text

Nonexistence of solutions for parabolic inequalities in unbounded cone-like domains via the test function method

Journal of Evolution Equations ◽

10.1007/pl00012600 ◽

2002 ◽

Vol 2 (4) ◽

pp. 459-470 ◽

Cited By ~ 5

Author(s):

Gennady G. Laptev

Keyword(s):

Function Method ◽

Test Function ◽

Nonexistence Of Solutions ◽

Test Function Method ◽

Parabolic Inequalities

Download Full-text

Nonexistence of solutions for quasilinear hyperbolic inequalities

Journal of Inequalities and Applications ◽

10.1186/s13660-021-02685-w ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Suping Xiao ◽

Zhong Bo Fang

Keyword(s):

Weak Solutions ◽

Function Method ◽

Source Term ◽

Cauchy Problems ◽

Global Weak Solutions ◽

Test Function ◽

Singular Source ◽

Nonexistence Of Solutions ◽

Test Function Method

AbstractIn this paper, we study the Cauchy problems for quasilinear hyperbolic inequalities with nonlocal singular source term and prove the nonexistence of global weak solutions in the homogeneous and nonhomogeneous cases by the test function method.

Download Full-text

Sharp upper bound for lifespan of solutions to some critical semilinear parabolic, dispersive and hyperbolic equations via a test function method

Nonlinear Analysis ◽

10.1016/j.na.2018.12.009 ◽

2019 ◽

Vol 182 ◽

pp. 57-74 ◽

Cited By ~ 13

Author(s):

Masahiro Ikeda ◽

Motohiro Sobajima

Keyword(s):

Upper Bound ◽

Function Method ◽

Hyperbolic Equations ◽

Test Function ◽

Semilinear Parabolic ◽

Test Function Method

Download Full-text

Bounded Solutions to Nonlinear Parabolic Equations

ISRN Mathematical Analysis ◽

10.5402/2011/574382 ◽

2011 ◽

Vol 2011 ◽

pp. 1-13

Author(s):

Jaouad Igbida

Keyword(s):

Parabolic Equations ◽

A Priori Estimates ◽

A Priori ◽

Nonlinear Parabolic Equations ◽

Bounded Solutions ◽

Test Function ◽

Nonlinear Parabolic ◽

Priori Estimates ◽

Compactness Arguments ◽

Test Function Method

We deal with existence results for nonlinear parabolic equations with general quadratic gradient terms and with absorption term which depend on the solution. We note that no boundedness is assumed on the data of the problem. We prove an existence result of distributional solution via test-function method. A priori estimates and compactness arguments are our main ingredient; the method of sub-supersolution does not apply her.

Download Full-text

Existence results of renormalized solutions for nonlinear $$p(\cdot )$$-parabolic equations with possibly singular measure data

Advances in Operator Theory ◽

10.1007/s43036-021-00139-0 ◽

2021 ◽

Vol 6 (3) ◽

Author(s):

Khadija Moutaouakil ◽

Jaouad Bennouna ◽

Bouchra El Hamdaoui ◽

Hicham Redwane

Keyword(s):

Parabolic Equations ◽

Existence Results ◽

Measure Data ◽

Renormalized Solutions ◽

Singular Measure

Download Full-text

Global nonexistence of solutions to degenerate parabolic equations in unbounded domains

Applied Mathematics Letters ◽

10.1016/j.aml.2005.07.009 ◽

2006 ◽

Vol 19 (6) ◽

pp. 535-540

Author(s):

Caisheng Chen

Keyword(s):

Parabolic Equations ◽

Unbounded Domains ◽

Degenerate Parabolic Equations ◽

Global Nonexistence ◽

Nonexistence Of Solutions ◽

Degenerate Parabolic

Download Full-text

Lump Solutions, Multi Lump Solutions and More Soliton Solutions of a Novel (2+1)-dimensional Nonlinear Evolution Equation

10.21203/rs.3.rs-996320/v1 ◽

2021 ◽

Author(s):

Hongcai Ma ◽

Shupan Yue ◽

Yidan Gao ◽

Aiping Deng

Keyword(s):

Evolution Equation ◽

Nonlinear Evolution Equation ◽

Nonlinear Evolution ◽

Three Dimensional ◽

Soliton Solutions ◽

Bilinear Method ◽

Test Function ◽

Lump Solutions ◽

Hirota Bilinear ◽

Test Function Method

Abstract Exact solutions of a new (2+1)-dimensional nonlinear evolution equation are studied. Through the Hirota bilinear method, the test function method and the improved tanh-coth and tah-cot method, with the assisstance of symbolic operations, one can obtain the lump solutions, multi lump solutions and more soliton solutions. Finally, by determining different parameters, we draw the three-dimensional plots and density plots at different times.

Download Full-text

Non-local problem with integral conditions for the three-dimensional high order hyperbolic equations

Вестник КРАУНЦ. Физико-математические науки ◽

10.26117/2079-6641-2020-33-4-51-62 ◽

2020 ◽

pp. 51-62

Author(s):

Ш.Ш. Юсубов

Keyword(s):

Integral Equation ◽

Hyperbolic Equation ◽

Hyperbolic Equations ◽

Three Dimensional ◽

High Order ◽

Mixed Derivative ◽

Local Problem ◽

Integral Conditions ◽

Order Hyperbolic Equation ◽

Non Local

В работе для трехмерного гиперболического уравнения высокого порядка с доминирующей смешанной производной исследуется разрешимость нелокальной задачи с интегральными условиями. Поставленная задача сводится к интегральному уравнению и с помощью априорных оценок доказывается существование единственного решения. In the work the solvability of the non-local problem with integral conditions is investigated for the three-dimensional high order hyperbolic equation with dominated mixed derivative. The problem is reduced to the integral equation and existence of the solution is proved by the help of aprior estimations.

Download Full-text