scholarly journals Regularized cosine existence and uniqueness families for second order abstract Cauchy problems

2002 ◽  
Vol 152 (2) ◽  
pp. 131-145 ◽  
Author(s):  
Jizhou Zhang
Keyword(s):  
Existence And Uniqueness ◽  
Second Order ◽  
Cauchy Problems ◽  
Abstract Cauchy Problems

scholarly journals On The Solvability of an Inverse Fractional Abstract Cauchy Problems with Conformable Derivative

2021 ◽  
Author(s):  
Lahcen Rabhi ◽  
Mohammed AL HORANI ◽  
R. Khalil
Keyword(s):  
Banach Space ◽  
Inverse Problem ◽  
Sobolev Space ◽  
Existence And Uniqueness ◽  
Parabolic Partial Differential Equations ◽  
Cauchy Problems ◽  
Conformable Derivative ◽  
Equivalent Statement ◽  
Special Cases ◽  
Abstract Cauchy Problems

In this paper, we discuss the solvability of fractional inverse problem for the conformable derivative in Banach space. We establish an equivalent statement of the existence and uniqueness of solution using fractional semigroup. Some special cases of the inverse problem are studied. An application is given to study an inverse problem in a suitable Sobolev space for fractional parabolic partial differential equations with unknown source functions.

scholarly journals On Cauchy problems for fuzzy differential equations

2004 ◽  
Vol 2004 (15) ◽  
pp. 799-805 ◽  
Author(s):  
D. N. Georgiou ◽  
I. E. Kougias
Keyword(s):  
Differential Equations ◽  
Existence And Uniqueness ◽  
Second Order ◽  
Uniqueness Theorems ◽  
Cauchy Problems ◽  
Existence And Uniqueness Theorems

Existence and uniqueness theorems are proved for Cauchy problems of second-order fuzzy differential equations.

scholarly journals Problem with data on the characteristics for a loaded system of hyperbolic equations

2021 ◽  
Vol 31 (3) ◽  
pp. 353-364
Author(s):  
A.T. Assanova ◽  
A. Zholamankyzy
Keyword(s):  
Approximate Solution ◽  
Initial Data ◽  
Existence And Uniqueness ◽  
Hyperbolic Equations ◽  
Rectangular Domain ◽  
Second Order ◽  
Cauchy Problems ◽  
Equivalent Problem ◽  
New Approach ◽  
Integral Relations

We consider a problem with data on the characteristics for a loaded system of hyperbolic equations of the second order on a rectangular domain. The questions of the existence and uniqueness of the classical solution of the considered problem, as well as the continuity dependence of the solution on the initial data, are investigated. We propose a new approach to solving the problem with data on the characteristics for the loaded system of hyperbolic equations second order based on the introduction new functions. By introducing new unknown functions the problem is reduced to an equivalent family of Cauchy problems for a loaded system of differential with a parameters and integral relations. An algorithm for finding an approximate solution to the equivalent problem is proposed and its convergence is proved. Conditions for the unique solvability of the problem with data on the characteristics for the loaded system of hyperbolic equations of the second order are established in the terms of coefficient's system.

scholarly journals Fractional Cauchy Problems for Infinite Interval Case-II

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1165
Author(s):  
Mohammed Al Horani ◽  
Mauro Fabrizio ◽  
Angelo Favini ◽  
Hiroki Tanabe
Keyword(s):  
Existence And Uniqueness ◽  
Direct Problem ◽  
Abstract Cauchy Problem ◽  
Continuous Functions ◽  
Cauchy Problems ◽  
Fractional Powers ◽  
Uniqueness Of Solutions ◽  
Infinite Intervals ◽  
Abstract Cauchy Problems ◽  
Densely Defined

We consider fractional abstract Cauchy problems on infinite intervals. A fractional abstract Cauchy problem for possibly degenerate equations in Banach spaces is considered. This form of degeneration may be strong and some convenient assumptions about the involved operators are required to handle the direct problem. Required conditions on spaces are also given, guaranteeing the existence and uniqueness of solutions. The fractional powers of the involved operator B X have been investigated in the space which consists of continuous functions u on [ 0 , ∞ ) without assuming u ( 0 ) = 0 . This enables us to refine some previous results and obtain the required abstract results when the operator B X is not necessarily densely defined.

scholarly journals Local k-convoluted c-semigroups and complete second order abstract Cauchy problems

Filomat ◽  
2018 ◽  
Vol 32 (19) ◽  
pp. 6789-6797 ◽  
Author(s):  
Chung-Cheng Kuo
Keyword(s):  
Integrable Function ◽  
Abstract Cauchy Problem ◽  
Second Order ◽  
Local Times ◽  
Cauchy Problems ◽  
Bounded Linear ◽  
Lipschitz Continuous ◽  
Locally Lipschitz ◽  
Locally Integrable Function ◽  
Abstract Cauchy Problems

Let C : X ? X be a bounded linear operator on a Banach space X over the field F(=R or C), and K : [0,T0)?F a locally integrable function for some 0 < T0 ? ?. Under some suitable assumptions, we deduce some relationship between the generation of a local (or an exponentially bounded) K-convoluted (C 0 0 C)-semigroup on X x X with subgenerator (resp., the generator) (0 I B A) and one of the following cases: (i) the well-posedness of a complete second-order abstract Cauchy problem ACP(A,B,f,x,y): w??(t) = Aw?(t) + Bw(t) + f (t) for a.e. t ?(0,T0) with w(0) = x and w?(0) = y; (ii) a Miyadera-Feller-Phillips-Hille- Yosida type condition; (iii) B is a subgenerator (resp., the generator) of a locally Lipschitz continuous local ?-times integrated C-cosine function on X for which A may not be bounded; (iv) A is a subgenerator (resp., the generator) of a local ?-times integrated C-semigroup on X for which B may not be bounded.

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