scholarly journals Nonexistence of Global Solutions for Coupled System of Pseudoparabolic Equations with Variable Exponents and Weak Memories

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Kh. Zennir ◽  
H. Dridi ◽  
S. Alodhaibi ◽  
S. Alkhalaf
Keyword(s):  
Boundary Value Problem ◽  
Blow Up ◽  
Modern Science ◽  
Global Solutions ◽  
Coupled System ◽  
Evolution System ◽  
Variable Exponents ◽  
Scientific Interest ◽  
Time Blowup ◽  
Pseudoparabolic Equations

The most important behavior for evolution system is the blow-up phenomena because of its wide applications in modern science. The article discusses the finite time blowup that arise under an appropriate conditions. The nonsolvability of boundary value problem for damped pseudoparabolic differential equations with variable exponents is investigated. Such problem has been previously studied in the case if p and q are constants. New here is the case of variables of nonlinearity p and q which make the problem has a scientific interest.

scholarly journals Blow-Up of Solutions with High Energies of a Coupled System of Hyperbolic Equations

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Jorge A. Esquivel-Avila
Keyword(s):  
Initial Data ◽  
Blow Up ◽  
Hyperbolic Equations ◽  
Sufficient Conditions ◽  
Global Solutions ◽  
Coupled System ◽  
Initial Energy ◽  
Evolution System ◽  
High Energies ◽  
Second Order In Time

We consider an abstract coupled evolution system of second order in time. For any positive value of the initial energy, in particular for high energies, we give sufficient conditions on the initial data to conclude nonexistence of global solutions. We compare our results with those in the literature and show how we improve them.

Blow-up of Solutions for a Semi-Linear Heat Equation with Variable Exponents

2013 ◽  
Vol 694-697 ◽  
pp. 699-702
Author(s):  
Ji Bing Zhang ◽  
Yun Zhu Gao
Keyword(s):  
Boundary Condition ◽  
Heat Equation ◽  
Blow Up ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Global Solutions ◽  
Variable Exponents ◽  
Linear Heat Equation ◽  
Linear Heat

In this paper, a semi-linear heat equation with nonlocal boundary condition and variable exponents is studied. The results to existence of global solutions or blow-up of solutions are obtained.

Global solutions and blowing-up solutions for a nonautonomous and nonlocal in space reaction-diffusion system with Dirichlet boundary conditions

2020 ◽  
Vol 23 (4) ◽  
pp. 1025-1053
Author(s):  
Marcos J. Ceballos-Lira ◽  
Aroldo Pérez
Keyword(s):  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Blow Up ◽  
Sufficient Conditions ◽  
Global Solutions ◽  
Coupled System ◽  
Dirichlet Boundary Conditions ◽  
Weakly Coupled System ◽  
Blowing Up ◽  
Fractional Diffusions

AbstractWe give sufficient conditions for global existence and finite time blow up of positive solutions for a nonautonomous weakly coupled system with distinct fractional diffusions and Dirichlet boundary conditions. Our approach is based on the intrinsic ultracontractivity property of the semigroups associated to distinct fractional diffusions and the study of blow up of a particular system of nonautonomus delay differential equations.

On the blow-up of solutions of a convective reaction diffusion equation

1993 ◽  
Vol 123 (3) ◽  
pp. 433-460 ◽  
Author(s):  
J. Aguirre ◽  
M. Escobedo
Keyword(s):  
Positive Solutions ◽  
Finite Time ◽  
Blow Up ◽  
Global Solutions ◽  
Reaction Diffusion ◽  
Scalar Function ◽  
Reaction Diffusion Equation ◽  
Semilinear Parabolic Equation ◽  
The Cauchy Problem ◽  
Image Position

SynopsisWe study the blow-up of positive solutions of the Cauchy problem for the semilinear parabolic equationwhere u is a scalar function of the spatial variable x ∈ ℝN and time t > 0, a ∈ ℝV, a ≠ 0, 1 < p and 1 ≦ q. We show that: (a) if p > 1 and 1 ≦ q ≦ p, there always exist solutions which blow up in finite time; (b) if 1 < q ≦ p ≦ min {1 + 2/N, 1 + 2q/(N + 1)} or if q = 1 and 1 < p ≦ l + 2/N, then all positive solutions blow up in finite time; (c) if q > 1 and p > min {1 + 2/N, 1 + 2q/N + 1)}, then global solutions exist; (d) if q = 1 and p > 1 + 2/N, then global solutions exist.

scholarly journals The structure of solutions to the pseudo-conformally invariant nonlinear Schrödinger equation

1991 ◽  
Vol 117 (3-4) ◽  
pp. 251-273 ◽  
Author(s):  
Thierry Cazenave ◽  
Fred B. Weissler
Keyword(s):  
Schrödinger Equation ◽  
Global Solution ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Blow Up ◽  
Global Solutions ◽  
Nonlinear Schrodinger Equation ◽  
Structure Of Solutions ◽  
Nonlinear Schrödinger ◽  
Conformally Invariant

SynopsisWe study solutions in ℝn of the nonlinear Schrödinger equation iut + Δu = λ |u|γu, where γ is the fixed power 4/n. For this particular power, these solutions satisfy the “pseudo-conformal” conservation law, and the set of solutions is invariant under a related transformation. This transformation gives a correspondence between global and non-global solutions (if λ < 0), and therefore allows us to deduce properties of global solutions from properties of non-global solutions, and vice versa. In particular, we show that a global solution is stable if and only if it decays at the same rate as a solution to the linear problem (with λ = 0). Also, we obtain an explicit formula for the inverse of the wave operator; and we give a sufficient condition (if λ < 0) that the blow up time of a non-global solution is a continuous function on the set of initial values with (for example) negative energy.

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