scholarly journals Théorie générale d’équation de type hyperbolique-parabolique non linéaire

2008 ◽  
Vol Volume 9, 2007 Conference in... ◽  
Author(s):  
Hamidou Touré
Keyword(s):  
Weak Solution ◽  
Group Theory ◽  
General Theory ◽  
Banach Spaces ◽  
Mild Solution ◽  
Existence Of Solutions ◽  
Parabolic Type ◽  
Semi Group ◽  
Nous Montrons ◽  
International Audience

International audience We develop general theory for degenerate hyperbolic-parabolic type problems using semi-group theory in Banach spaces. We establish existence, uniqness results and continuous dependance with respects to data for mild solution. Similar results are developped for weak solution of entropy type, and existence of solutions are studied. Nous développons une théorie générale pour des équations d’évolution de type hyperbolique parabolique non linéaire à l’aide de la théorie des semi-groupes non linéaires dans les espaces de Banach. Nous établissons des résultats d’existence, d’unicité et de dépendance continue par rapport aux données d’une bonne solution du problème de Cauchy ou des problèmes aux limites associées à cette équation sous des hypothèses très générales. Avec des hypothèses complémentaires, nous montrons que cette bonne solution est une solution locale de type entropique, nous étudions également l’unicité des solutions faibles et l’existence de solution forte.

scholarly journals Existence results for an impulsive neutral integro-differential equations in Banach spaces

2019 ◽  
Vol 27 (3) ◽  
pp. 231-257
Author(s):  
Venkatesh Usha ◽  
Dumitru Baleanu ◽  
Mani Mallika Arjunan
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Group Theory ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Banach Spaces ◽  
Mild Solution ◽  
Existence Results ◽  
Semi Group ◽  
Schaefer Fixed Point Theorem

AbstractIn this manuscript we investigate the existence of mild solution for a abstract impulsive neutral integro-differential equation by using semi-group theory and Krasnoselskii-Schaefer fixed point theorem in different approach. At last, an example is also provided to illustrate the obtained results.

scholarly journals Existence of Fractional Impulsive Functional Integro-Differential Equations in Banach Spaces

2018 ◽  
Author(s):  
Dimplekumar Chalishajar ◽  
C. Ravichandran ◽  
S. Dhanalakshmi ◽  
R. Murugesu
Keyword(s):  
Fixed Point ◽  
Group Theory ◽  
Differential Equations ◽  
Banach Spaces ◽  
Mild Solution ◽  
Fixed Point Theorems ◽  
Mild Solutions ◽  
Semi Group ◽  
Finite Delay ◽  
Non Local

In this paper, we established the existence of PC-mild solutions for non local fractional impulsive functional integro-differential equations with finite delay. The proofs are obtained by using the techniques of fixed point theorems, semi-group theory and generalized Bellman inequality. In this paper, we have used the distributed characteristic operators to define the mild solution of the system. Results obtained here improve and extend some known results.

scholarly journals Existence of Fractional Impulsive Functional Integro-Differential Equations in Banach Spaces

2019 ◽  
Vol 2 (2) ◽  
pp. 18 ◽  
Author(s):  
Dimplekumar Chalishajar ◽  
Chokkalingam Ravichandran ◽  
Shanmugam Dhanalakshmi ◽  
Rangasamy Murugesu
Keyword(s):  
Fixed Point ◽  
Group Theory ◽  
Differential Equations ◽  
Banach Spaces ◽  
Fractional Order ◽  
Fixed Point Theorems ◽  
Mild Solutions ◽  
Order System ◽  
Semi Group ◽  
Non Local

In this paper, we establish the existence of piece wise (PC)-mild solutions (defined in Section 2) for non local fractional impulsive functional integro-differential equations with finite delay. The proofs are obtained using techniques of fixed point theorems, semi-group theory and generalized Bellman inequality. In this paper, we used the distributed characteristic operators to define a mild solution of the system. We also discussed the controversy related to the solution operator for the fractional order system using weak and strong Caputo derivatives. Examples are given to illustrate the theory.

On the non-existence of semi-groups for some equations of continuum mechanics

1980 ◽  
Vol 86 (3-4) ◽  
pp. 303-306 ◽  
Author(s):  
N. S. Wilkes
Keyword(s):  
Group Theory ◽  
Continuum Mechanics ◽  
Linear Elasticity ◽  
Existence Of Solutions ◽  
Elasticity Tensor ◽  
Positive Definite ◽  
Semi Group

SynopsisLinear semi-group theory can be used to prove the existence of solutions to the equations of linear elasticity when the elasticity tensor is positive definite. Here, it is shown that this condition is also necessary for the existence of a semi-group. The method is also applied to linear dissipative equations.

scholarly journals Existence and optimal controls for nonlocal fractional evolution equations of order (1,2) in Banach spaces

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Denghao Pang ◽  
Wei Jiang ◽  
Azmat Ullah Khan Niazi ◽  
Jiale Sheng
Keyword(s):  
Banach Spaces ◽  
Mild Solution ◽  
Measure Of Noncompactness ◽  
Evolution Equations ◽  
Well Posedness ◽  
Optimal Controls ◽  
Lagrange Problem ◽  
Fractional Differential ◽  
Fractional Evolution Systems ◽  
Definition Of

AbstractIn this paper, we mainly investigate the existence, continuous dependence, and the optimal control for nonlocal fractional differential evolution equations of order (1,2) in Banach spaces. We define a competent definition of a mild solution. On this basis, we verify the well-posedness of the mild solution. Meanwhile, with a construction of Lagrange problem, we elaborate the existence of optimal pairs of the fractional evolution systems. The main tools are the fractional calculus, cosine family, multivalued analysis, measure of noncompactness method, and fixed point theorem. Finally, an example is propounded to illustrate the validity of our main results.

scholarly journals Existence of solutions for functional boundary value problems at resonance on the half-line

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Bingzhi Sun ◽  
Weihua Jiang
Keyword(s):  
Boundary Value Problems ◽  
Banach Spaces ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Half Line ◽  
Projection Scheme ◽  
At Resonance ◽  
Functional Boundary

Abstract By defining the Banach spaces endowed with the appropriate norm, constructing a suitable projection scheme, and using the coincidence degree theory due to Mawhin, we study the existence of solutions for functional boundary value problems at resonance on the half-line with $\operatorname{dim}\operatorname{Ker}L = 1$ dim Ker L = 1 . And an example is given to show that our result here is valid.

Some Results from the General Theory of Banach Spaces

1997 ◽  
pp. 71-86
Author(s):  
Mikhail I. Kadets ◽  
Vladimir M. Kadets
Keyword(s):  
General Theory ◽  
Banach Spaces

scholarly journals Macdonald polynomials at $t=q^k$

2009 ◽  
Vol DMTCS Proceedings vol. AK,... (Proceedings) ◽  
Author(s):  
Jean-Gabriel Luque
Keyword(s):  
Macdonald Polynomials ◽  
Nous Montrons ◽  
International Audience

International audience We investigate the homogeneous symmetric Macdonald polynomials $P_{\lambda} (\mathbb{X} ;q,t)$ for the specialization $t=q^k$. We show an identity relying the polynomials $P_{\lambda} (\mathbb{X} ;q,q^k)$ and $P_{\lambda} (\frac{1-q}{1-q^k}\mathbb{X} ;q,q^k)$. As a consequence, we describe an operator whose eigenvalues characterize the polynomials $P_{\lambda} (\mathbb{X} ;q,q^k)$. Nous nous intéressons aux propriétés des polynômes de Macdonald symétriques $P_{\lambda} (\mathbb{X} ;q,t)$ pour la spécialisation $t=q^k$. En particulier nous montrons une égalité reliant les polynômes $P_{\lambda} (\mathbb{X} ;q,q^k)$ et $P_{\lambda} (\frac{1-q}{1-q^k}\mathbb{X} ;q,q^k)$. Nous en déduisons la description d'un opérateur dont les valeurs propres caractérisent les polynômes $P_{\lambda} (\mathbb{X} ;q,q^k)$.

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