Some properties of the heat-transfer process in a motionless medium, taking account of heat-flux relaxation

Levanov, E. I.; Sotskii, E. N.

doi:10.1007/bf00871550

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Discontinuous Solution1

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2013

2024

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Cited by 2 publications

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“…We define the function γ according to the scheme outlined in [64,65,66]. But first, following [67], we rewrite Eq. (1.1), (6.3) in a conservative form…”

Section: Discontinuous Solutionmentioning

confidence: 99%

Classical Solutions of a Mixed Problem with the Zaremba Boundary Condition for a Mildly Quasilinear Wave Equation

Korzyuk,

Rudzko

2024

Preprint

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For a mildly nonlinear wave equation given in the first quadrant, we consider a mixed problem in which we pose the Cauchy conditions on the spatial half-line and the Zaremba condition on the time half-line. Using the method of characteristics, we construct the solution in an implicit analytical form as a solution of some integro-differential equations. The solvability of these equations is studied, as well as the dependence on the initial data and the smoothness of their solutions. For the problem in question, the uniqueness of the solution is proved, and the conditions under which its classical solution exists are established. If the compatibility conditions are not satisfied, then we consider a problem with conjugation conditions. We construct a mild solution if the data are not smooth enough. We apply the obtained mathematical results to solve a problem from combustion theory. Mathematics Subject Classification (2010). Primary 35L20; Secondary 35A02, 35A09, 35D99, 35L71, 35Q79, 80A25.

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“…We define the function γ according to the scheme outlined in [64,65,66]. But first, following [67], we rewrite Eq. (1.1), (6.3) in a conservative form…”

Section: Discontinuous Solutionmentioning

confidence: 99%

Classical Solutions of a Mixed Problem with the Zaremba Boundary Condition for a Mildly Quasilinear Wave Equation

Korzyuk,

Rudzko

2024

Preprint

View full text Add to dashboard Cite

show abstract

Analysis of the wave propagation processes in heat transfer problems of the hyperbolic type

Babenkov

Иванова

2013

Continuum Mech. Thermodyn.

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Some properties of the heat-transfer process in a motionless medium, taking account of heat-flux relaxation

Cited by 2 publications

References 6 publications

Classical Solutions of a Mixed Problem with the Zaremba Boundary Condition for a Mildly Quasilinear Wave Equation

Classical Solutions of a Mixed Problem with the Zaremba Boundary Condition for a Mildly Quasilinear Wave Equation

Analysis of the wave propagation processes in heat transfer problems of the hyperbolic type

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