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Averaging of Higher-Order Parabolic Equations with Periodic Coefficients
Современная математика: Фундаментальные направления, 2021 In L2(Rd;Cn), we consider a wide class of matrix elliptic operators Aε of order 2p (where p≥2) with periodic rapidly oscillating coefficients (depending on x/ε). Here ε 0 is a small parameter.
A. A. Miloslova, T. A. Suslina
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Boundary Value Problems, 2021 In this paper, we study the initial boundary value problem for a class of higher-order n-dimensional nonlinear pseudo-parabolic equations which do not have positive energy and come from the soil mechanics, the heat conduction, and the nonlinear optics ...
Liming Xiao, Mingkun Li
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Applications of higher-order parabolic equations [PDF]
The Journal of the Acoustical Society of America, 1989 The parabolic equation (PE) model is very useful for many range-dependent acoustic calculations. However, the PE solution breaks down for propagation at large angles, out to long ranges, and in domains in which sound-speed variations are relatively large.
M. D. Collins
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Higher-order parabolic equations without conditions at infinity
Journal of Mathematical Analysis and Applications, 2002 This paper is devoted to the following Cauchy problem: \[ \begin{cases} \rho\frac {\partial u}{\partial t}=\sum^m_{k=0}(-1)^{k+1} \frac {\partial^k}{\partial x^k} \left(a_k\frac {\partial^ku}{\partial x^k} \right)- c_0| u|^{p-1}u\quad &\text{in }S=\mathbb{R}\times(0,T)\\ u=u_0\quad &\text{in }\mathbb{R}\times \{0\},\end{cases}\tag{1} \] where \(p>1\), \
MARCHI, CLAUDIO, TESEI A.
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ENERGY-CONSERVING AND RECIPROCAL SOLUTIONS FOR HIGHER-ORDER PARABOLIC EQUATIONS
Journal of Computational Acoustics, 1999 The energy conservation law and the flow reversal theorem are valid for underwater acoustic fields. In media at rest the theorem transforms into well-known reciprocity principle. The presented parabolic equation (PE) model strictly preserves these important physical properties in the numerical solution.
D. Mikhin
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Nonlocal Boundary Conditions for Higher–Order Parabolic Equations [PDF]
PAMM, 2006 AbstractThis work deals with the efficient numerical solution of the two–dimensional one–way Helmholtz equation posed on an unbounded domain. In this case one has to introduce artificial boundary conditions to confine the computational domain. Here we construct with the Z –transformation so–called discrete transparent boundary conditions for higher ...
Matthias Ehrhardt, Andrea Zisowsky
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On the Dirichlet problem for certain higher order parabolic equations [PDF]
Pacific Journal of Mathematics, 1960 R. K. Juberg
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Entropy dissipative higher order accurate positivity preserving time-implicit discretizations for nonlinear degenerate parabolic equations [PDF]
Journal of Computational and Applied Mathematics, 2023 We develop entropy dissipative higher order accurate local discontinuous Galerkin (LDG) discretizations coupled with Diagonally Implicit Runge-Kutta (DIRK) methods for nonlinear degenerate parabolic equations with a gradient flow structure.
F. Yan, J. V. D. Vegt, Y. Xia, Y. Xu
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Pointwise-in-time a posteriori error control for higher-order discretizations of time-fractional parabolic equations [PDF]
Journal of Computational and Applied Mathematics, 2022 Time-fractional parabolic equations with a Caputo time derivative are considered. For such equations, we explore and further develop the new methodology of the a-posteriori error estimation and adaptive time stepping proposed in [7].
S. Franz, N. Kopteva
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Математичні Студії, 2023 Initial-boundary value problems for parabolic and elliptic-parabolic (that is degenerated parabolic) equations in unbounded domains with respect to the spatial variables were studied by many authors.
M. M. Bokalo, O. V. Domanska
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