scholarly journals Global well-posedness of the KP-I initial-value problem in the energy space

2008 ◽  
Vol 173 (2) ◽  
pp. 265-304 ◽  
Author(s):  
A.D. Ionescu ◽  
C.E. Kenig ◽  
D. Tataru
Keyword(s):  
Initial Value Problem ◽  
Energy Space ◽  
Well Posedness ◽  
Initial Value

scholarly journals ENERGY CRITICAL NLS IN TWO SPACE DIMENSIONS

2009 ◽  
Vol 06 (03) ◽  
pp. 549-575 ◽  
Author(s):  
J. COLLIANDER ◽  
S. IBRAHIM ◽  
M. MAJDOUB ◽  
N. MASMOUDI
Keyword(s):  
Schrödinger Equation ◽  
Initial Value Problem ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Energy Space ◽  
Well Posedness ◽  
Initial Value ◽  
Exponential Nonlinearity ◽  
Supercritical Case ◽  
Two Space Dimensions

We investigate the initial value problem for a defocusing nonlinear Schrödinger equation with exponential nonlinearity [Formula: see text] We identify subcritical, critical, and supercritical regimes in the energy space. We establish global well-posedness in the subcritical and critical regimes. Well-posedness fails to hold in the supercritical case.

Asymptotics for a class of heat equations with inhomogeneous nonlinearity

Analysis ◽  
2018 ◽  
Vol 38 (1) ◽  
pp. 21-36
Author(s):  
Tarek Saanouni ◽  
Radhia Ghanmi
Keyword(s):  
Heat Equation ◽  
Initial Value Problem ◽  
Energy Space ◽  
Nonlinear Heat Equation ◽  
Heat Equations ◽  
Well Posedness ◽  
Initial Value ◽  
Power Nonlinearity

AbstractThe initial value problem for an inhomogeneous nonlinear heat equation with a pure power nonlinearity is investigated. In the radial energy space, global and non-global well-posedness are discussed.

scholarly journals Some Mathematical Aspects of f(R)-Gravity with Torsion: Cauchy Problem and Junction Conditions

Universe ◽  
2019 ◽  
Vol 5 (12) ◽  
pp. 224 ◽  
Author(s):  
Stefano Vignolo
Keyword(s):  
Cauchy Problem ◽  
Initial Value Problem ◽  
Sufficient Conditions ◽  
Well Posedness ◽  
Junction Conditions ◽  
Field Equations ◽  
Initial Value ◽  
The Cauchy Problem ◽  
General Conditions

We discuss the Cauchy problem and the junction conditions within the framework of f ( R ) -gravity with torsion. We derive sufficient conditions to ensure the well-posedness of the initial value problem, as well as general conditions to join together on a given hypersurface two different solutions of the field equations. The stated results can be useful to distinguish viable from nonviable f ( R ) -models with torsion.

scholarly journals Well-Posedness and Time Regularity for a System of Modified Korteweg-de Vries-Type Equations in Analytic Gevrey Spaces

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 809
Author(s):  
Aissa Boukarou ◽  
Kaddour Guerbati ◽  
Khaled Zennir ◽  
Sultan Alodhaibi ◽  
Salem Alkhalaf
Keyword(s):  
Unique Solution ◽  
Initial Value Problem ◽  
Coupled System ◽  
Well Posedness ◽  
Initial Value ◽  
Gevrey Spaces ◽  
De Vries ◽  
Gevrey Space

Studies of modified Korteweg-de Vries-type equations are of considerable mathematical interest due to the importance of their applications in various branches of mechanics and physics. In this article, using trilinear estimate in Bourgain spaces, we show the local well-posedness of the initial value problem associated with a coupled system consisting of modified Korteweg-de Vries equations for given data. Furthermore, we prove that the unique solution belongs to Gevrey space G σ × G σ in x and G 3 σ × G 3 σ in t. This article is a continuation of recent studies reflected.

scholarly journals Remarks on the critical nonlinear high-order heat equation

2019 ◽  
Vol 26 (1/2) ◽  
pp. 127-152
Author(s):  
Tarek Saanouni
Keyword(s):  
Global Existence ◽  
Heat Equation ◽  
Initial Value Problem ◽  
Existence Of Solutions ◽  
High Order ◽  
Well Posedness ◽  
Potential Well ◽  
Initial Value ◽  
Global Existence Of Solutions ◽  
Nonlinear High Order

The initial value problem for a semi-linear high-order heat equation is investigated. In the focusing case, global well-posedness and exponential decay are obtained. In the focusing sign, global and non global existence of solutions are discussed via the potential well method.

WELL-POSEDNESS AND BLOWUP PHENOMENA FOR A THREE-COMPONENT CAMASSA–HOLM SYSTEM WITH PEAKONS

2012 ◽  
Vol 09 (03) ◽  
pp. 451-467 ◽  
Author(s):  
QIAOYI HU ◽  
LIYUN LIN ◽  
JI JIN
Keyword(s):  
Initial Value Problem ◽  
Strong Solutions ◽  
Well Posedness ◽  
Initial Value ◽  
Blowup Rate ◽  
Holm Equation ◽  
Two Component

First, we establish the local well-posedness of the initial value problem for a new three-component Camassa–Holm system with peakons. We then present a precise blowup scenario and several blowup results for strong solutions to that system. Finally, we determine the blowup rate of strong solutions to the system when a blowup occurs. Our results include all earlier results on the Camassa–Holm equation and on a two-component Camassa–Holm system with peakons.

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