Exactly solvable Burgers type equations with variable coefficients and moving boundary conditions

tarafından

Bozacı Serdal, Aylin, author.

Başlık

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Exactly solvable Burgers type equations with variable coefficients and moving boundary conditions

Yazar

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Bozacı Serdal, Aylin, author.

Yazar Ek Girişi

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Bozacı Serdal, Aylin, author.

Fiziksel Tanımlama

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xiii, 201 leaves: charts;+ 1 computer laser optical disc.

Özet

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In this thesis, firstly, a generalized diffusion type equation is considered. A family of analytical solutions to an initial value problem on the whole line for this equation is obtained in terms of solutions to the characteristic ordinary differential equation and the standard heat model by using Wei-Norman Lie algebraic approach for finding the evolution operator of the associated diffusion type equation. Then, initial-boundary value problems on half-line and an initial-boundary value problem with moving boundary for this equation are studied. It is shown that if the boundary propagates according to an associated classical equation of motion determined by the time-dependent parameters, then the analytical solution is obtained in terms of the heat problem on the half-line. For this, a non-linear Riccati type dynamical system, that simultaneously determines the solution of the diffusion type problem and the moving boundary is solved by a linearization procedure. The mean position of the solutions, the influence of the moving boundaries and the variable parameters are examined by constructing exactly solvable models. Then, an initial value problem for a generalized Burgers type equation on whole real line is discussed. By using Cole-Hopf linearization and solution of the corresponding generalized linear diffusion type equation, a family of analytical solution is obtained in terms of solutions to the characteristic equation and the standard heat or Burgers model. Exactly solvable models are constructed and the influence of the variable coefficients are examined. Later, an initial-boundary value problem for the generalized Burgers type equation with Dirichlet boundary condition defined on the half-line is studied. Finally, an initial-boundary value problem for the generalized Burgers type equations with Dirichlet boundary condition imposed at a moving boundary is considered. The analytical solution is obtained in terms of solution to characteristic equation and the standard heat or Burgers model, if the moving boundary propagates according to an associated classical equation of motion. In order to show certain aspects of the general results, some exactly solvable models are introduced and solutions corresponding to different types of initial and homogeneous/inhomogeneous boundary conditions are discussed by examining the influence of the moving boundaries.

Konu Başlığı

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Burgers equation.

Heat equation

Yazar Ek Girişi

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Atılgan Büyükaşık, Şirin,

Tüzel Kişi Ek Girişi

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İzmir Institute of Technology. Mathematics.

Tek Biçim Eser Adı

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Thesis (Doctoral)--İzmir Institute of Technology: Mathematics.

İzmir Institute of Technology: Mathematics--Thesis (Doctoral).

Elektronik Erişim

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Library | Materyal Türü | Demirbaş Numarası | Yer Numarası | Durumu/İade Tarihi |
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IYTE Library | Tez | T002678 | QA377 .B79 2022 | Tez Koleksiyonu |