Problem with integral condition for a partial differential equation of the first order with respect to time

Kalenyuk, P. І.; Kohut, І. V.; Nytrebych, Zinovii

doi:10.1007/s10958-012-0685-7

Cited by 12 publications

(5 citation statements)

References 6 publications

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“…Theorem 3.1. Let the right-hand sides φ 0 (x) and φ 1 (x) of conditions (12) belong to K M and have the form (18). Then the solution of problem (11), (12) in the class of quasi-polynomials K C,M exists and it can be written in the form…”

Section: Resultsmentioning

confidence: 99%

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The differential-symbol method of constructing the quasi-polynomial solutions of two-point problem

Nytrebych

Маланчук

2019

Demonstratio Mathematica

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The solvability of the problem with local nonhomogeneous two-point in time conditions for a homogeneous PDE of the second order in time and infinite order in spatial variable in the case when the set of zeroes of the characteristic determinant is not empty and does not coincide with C is investigated. The existence of a solution of the problem in which the right-hand sides of the two-point conditions are quasi-polynomials is proved. We propose the differential-symbol method of constructing the solutions of the problem.

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Section: Resultsmentioning

confidence: 99%

“…, 0). The problems for PDEs with conditions in time variables by using the differentialsymbol method were studied in [18][19][20][21]. Symbol calculus which is inherent for differential-symbol method we can see, for example, in papers [22,23].…”

Section: Introductionmentioning

confidence: 99%

The differential-symbol method of constructing the quasi-polynomial solutions of two-point problem

Nytrebych

Маланчук

2019

Demonstratio Mathematica

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“…The present work is a continuation of the investigations carried out in [3,5]. We propose a method for the solution of a problem with inhomogeneous integral conditions for a homogeneous differential-operator equation with abstract operator in a linear space.…”

Section: Introductionmentioning

confidence: 90%

Problem with Integral Conditions for Differential-Operator Equation

et al. 2015

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We propose a method for the solution of the problem with inhomogeneous integral conditions for homogeneous differential-operator equations with abstract operator in a linear space H . For the righthand sides of the integral conditions from a special subspace L ⊆ H in which the vectors are represented in the form of Stieltjes integrals with respect to certain measures, the solution of the problem is represented in the form of Stieltjes integrals with respect to the same measures. We give an example of application of the method to the solution of the ill-posed problem for the second-order partial differential equation in the time variable (in which the integral conditions are given) and, in general, an infiniteorder partial differential equation in the space variable.

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“…To solve the problem, it is appropriate to apply a differential-symbol method. Note that a given method has been effectively used earlier to solve similar problems with linear conditions based on the selected time variable (under initial conditions in [40,41], integral conditions in [42], the Dirichlet conditions in [43], and local two-point conditions in [44,45]).…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

Analytical method to study a mathematical model of wave processes under twopoint time conditions

Nytrebych

Ільків

Пукач

et al. 2019

EEJET

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Adequate mathematical modeling of wave processes in oscillatory systems plays an important role in modern approaches to solving a series of scientific and engineering tasks, which arise in the problems on analysis, synthesis, and optimization of parameters for machine-building structures. Mathematical and numerical modelling are important in understanding the essence of phenomena and processes that are studied in modern mechanics and physics. Considering the adequacy of mathematical models and methods of analysis contributes to the interpretation of existing, as well as prediction and discovery of new, phenomena. Modern industrial equipment is operated in a wide range of parameters, particularly at high speeds, high pressures and energies, etc. The specified reasons necessitate the study and analysis

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Problem with integral condition for a partial differential equation of the first order with respect to time

Cited by 12 publications

References 6 publications

The differential-symbol method of constructing the quasi-polynomial solutions of two-point problem

The differential-symbol method of constructing the quasi-polynomial solutions of two-point problem

Problem with Integral Conditions for Differential-Operator Equation

Analytical method to study a mathematical model of wave processes under twopoint time conditions

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Problem with integral condition for a partial differential equation of the first order with respect to time

Cited by 12 publications

References 6 publications

The differential-symbol method of constructing the quasi-polynomial solutions of two-point problem

The differential-symbol method of constructing the quasi-polynomial solutions of two-point problem

Problem with Integral Conditions for Differential-Operator Equation

Analytical method to study a mathematical model of wave processes under two­point time conditions

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Product

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Analytical method to study a mathematical model of wave processes under twopoint time conditions