scholarly journals Determining of right-hand side of higher order ultraparabolic equation

2017 ◽  
Vol 15 (1) ◽  
pp. 1048-1062 ◽  
Author(s):  
Nataliya Protsakh
Keyword(s):  
Inverse Problem ◽  
Existence And Uniqueness ◽  
Higher Order ◽  
Integral Type ◽  
Ultraparabolic Equation ◽  
Right Hand ◽  
Uniqueness Of The Solution ◽  
Time Variables

Abstract In the paper the conditions of the existence and uniqueness of the solution for the inverse problem for higher order ultraparabolic equation are obtained. The equation contains two unknown functions of spatial and time variables in its right-hand side. The overdetermination conditions of the integral type are used.

scholarly journals On the existence and uniqueness of the solution of the coefficient inverse problem for a semilinear parabolic equation

2021 ◽  
Vol 2092 (1) ◽  
pp. 012008
Author(s):  
A L Sugezhik
Keyword(s):  
Inverse Problem ◽  
Parabolic Equation ◽  
Existence And Uniqueness ◽  
Input Data ◽  
Source Function ◽  
Semilinear Parabolic Equation ◽  
Coefficient Inverse Problem ◽  
Uniqueness Of The Solution ◽  
Bounded Functions ◽  
Semilinear Parabolic

Abstract In this paper, we consider the problem of determining the source function and the coefficient by the derivative with respect to time in a semilinear parabolic equation with overdetermination conditions defined on two different hyperplanes. The existence and uniqueness theorems of the classical solution of the posed coefficient inverse problem in the class of smooth bounded functions were proved. An example of input data satisfying the conditions of the proved theorems is given.

scholarly journals Around Chaotic Disturbance and Irregularity for Higher Order Traveling Waves

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Emile F. Doungmo Goufo ◽  
Ignace Tchangou Toudjeu
Keyword(s):  
Traveling Waves ◽  
Existence And Uniqueness ◽  
Scientific Community ◽  
Wave Motion ◽  
Solitary Wave Solution ◽  
Kdv Equation ◽  
Perturbation Parameter ◽  
Higher Order ◽  
Uniqueness Of The Solution ◽  
Seventh Order

Many unknown features in the theory of wave motion are still captivating the global scientific community. In this paper, we consider a model of seventh order Korteweg–de Vries (KdV) equation with one perturbation level, expressed with the recently introduced derivative with nonsingular kernel, Caputo-Fabrizio derivative (CFFD). Existence and uniqueness of the solution to the model are established and proven to be continuous. The model is solved numerically, to exhibit the shape of related solitary waves and perform some graphical simulations. As expected, the solitary wave solution to the model without higher order perturbation term is shown via its related homoclinic orbit to lie on a curved surface. Unlike models with conventional derivative (γ=1) where regular behaviors are noticed, the wave motions of models with the nonsingular kernel derivative are characterized by irregular behaviors in the pure factional cases (γ<1). Hence, the regularity of a soliton can be perturbed by this nonsingular kernel derivative, which, combined with the perturbation parameter ζ of the seventh order KdV equation, simply causes more accentuated irregularities (close to chaos) due to small irregular deviations.

scholarly journals Inverse problem for semilinear Eidelman type equation

2020 ◽  
Vol 53 (1) ◽  
pp. 48-58
Author(s):  
N.P. Protsakh ◽  
O. E. Parasiuk-Zasun
Keyword(s):  
Inverse Problem ◽  
Weak Solution ◽  
Sufficient Conditions ◽  
Type Equation ◽  
Initial Boundary ◽  
Time Dependent ◽  
Integral Type ◽  
Dependent Function ◽  
Right Hand

The inverse problem for semilinear Eidelman type equation with unknown time dependent function in its right-hand side is considered in this paper. The initial, boundary and integral type overdetermination conditions are posed. The sufficient conditions of the existence and the uniqueness of weak solution for the problem are obtained.

scholarly journals Determining of unknown functions of different arguments in minor coefficient and right-hand side of semilinear ultraparabolic equation

2020 ◽  
Vol 12 (2) ◽  
pp. 317-332
Author(s):  
N.P. Protsakh ◽  
V.M. Flyud
Keyword(s):  
Inverse Problem ◽  
Sufficient Conditions ◽  
Uniqueness Of Solution ◽  
Ultraparabolic Equation ◽  
Right Hand

In this paper, we consider the inverse problem for semilinear ultraparabolic equation. The equation has two unknown functions of different arguments in its minor coefficient and in right-hand side function. The sufficient conditions of the existence and the uniqueness of solution on some interval $[0,T],$ where $T$ depends on the coefficients of the equation, are obtained.

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