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Note on a higher order pseudo‐parabolic equation with variable exponents
Mathematical Methods in the Applied Sciences, 2023In this paper, we study a higher order pseudo‐parabolic equation involving ‐Laplacian with the Navier boundary condition. We use the energy method, the Sobolev embedding inequalities and the Galerkin's approximation to show the classification of singular solutions, including the existence and nonexistence of global, blow‐up, and extinction solutions ...
Bingchen Liu, Yang Li
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Linear and semilinear higher order parabolic equations in
Nonlinear Analysis: Theory, Methods & Applications, 2012Abstract In this paper we consider some fourth order linear and semilinear equations in R N and make a detailed study of the solvability of the Cauchy problem. For the linear equation we consider some weakly integrable potential terms, and for any 1 p ∞ prove that for a suitable family of Bessel potential spaces, H p
Jan W. Cholewa, Anibal Rodriguez-Bernal
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Parabolicity of a Class of Higher-Order Abstract Differential Equations
Proceedings of the American Mathematical Society, 1994Summary: Let \(E\) be a complex Banach space, \(c_ i\in \mathbb{C}\) \((1\leq i\leq n- 1)\), and \(A\) be a nonnegative operator in \(E\). We discuss the parabolicity of the higher-order abstract differential equations \[ u^{(n)}(t)+ \sum^{n- 1}_{i= 1} c_ i A^{k_ i} u^{(n- i)}(t)+ Au(t)= 0\leqno{(*)} \] and some perturbation cases of \((*)\).
Xio, Tijun, Liang, Jin
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Benchmark calculations for higher-order parabolic equations
The Journal of the Acoustical Society of America, 1990Benchmark solutions generated with parabolic equation (PE) models are presented for range-dependent underwater acoustic propagation problems involving both penetrable and perfectly reflecting ocean bottoms. The solution of the wide-angle PE of Claerbout [J. F. Claerbout, Fundamentals of Geophysical Data Processing (McGraw-Hill, New York, 1976), pp. 206–
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Self-Similar Blow-Up in Higher-Order Semilinear Parabolic Equations
SIAM Journal on Applied Mathematics, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Budd, C. J. +2 more
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On higher order parabolic functional differential equations
Periodica Mathematica Hungarica, 1995The author proves existence of weak solutions of the higher-order parabolic functional differential equation \[ D_tu+\sum_{|\alpha|\leq m}(-1)^{|\alpha|}D^\alpha_x[f_\alpha(t,x,u,\dots, D^\beta_xu,\dots)]+ \sum_{|\alpha|\leq m}(-1)^{|\alpha|}D^\alpha_x[g_\alpha(t,x,u,\dots, D^\gamma_xu,\dots)]+ \] \[ \sum_{|\alpha|\leq m}(-1)^{|\alpha|} \int^t_{t-r}D ...
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On Doubly Degenerate Quasilinear Parabolic Equations of Higher Order
Acta Mathematica Sinica, English Series, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On degenerate quasilinear parabolic equations of higher order
Periodica Mathematica Hungarica, 1996zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Higher-order parabolic approximations to time-independent wave equations
Journal of Mathematical Physics, 1983A sequence of numerically tractable higher-order parabolic approximations is derived for the reduced wave equation in an inhomogeneous medium. The derivation is motivated by a definition of waves propagating in a distinguished direction. For a homogeneous medium these definitions are exact and yield uncoupled, infinite-order parabolic equations which ...
Corones, J. P., Krueger, R. J.
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A splitting procedure for parabolic equations of higher order
International Journal of Computer Mathematics, 1983In this paper, the numerical solution of parabolic equations of order n is shown to be easily accomplished by a splitting procedure involving the use of n computational nets.
D.J. Evans, A. Danaee
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