Results 1 to 10 of about 6,797 (118)

Unique Continuation for Parabolic Equations of Higher Order [PDF]

Nagoya Mathematical Journal, 1966
Let x = (xl,…xn) be a point in the n-dimensional Euclidean space and let be the unit sphere In the (n + 1)-dimensional Euclidean space with coordinate (x, t), we putandwhere denotes the boundary of . We also use the following notation:
Chen, Lu-san, Kuroda, Tadashi
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On the numerical solution of higher order nonlinear parabolic equations [PDF]

Computing, 1968
This paper deals with the numerical approximation of weak solutions of the first initial, boundary value problem for the higher order, nonlinear parabolic equation $$\sum\limits_{|\alpha | , |\beta | \leqq p} {D^\alpha (a_{\alpha \beta } (x,t)) \leqq D^\beta u - \partial u/
Eugene L. Allgower, Ronald Guenther
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Parabolicity of a Class of Higher-Order Abstract Differential Equations [PDF]

Proceedings of the American Mathematical Society, 1994
Summary: 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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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.
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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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Higher order linear parabolic equations

, 2012
We first highlight the main differences between second order and higher order linear parabolic equations. Then we survey existing results for the latter, in particular by analyzing the behavior of the convolution kernels. We illustrate the updated state of art and we suggest several open problems.
G. Barbatis, GAZZOLA, FILIPPO
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Asymptotic behavior of solutions of parabolic equations of higher order [PDF]

Pacific Journal of Mathematics, 1966
By use of a priori integral estimates like those used in the author and \textit{T. Kuroda} [Nagoya Math. J. 26, 115--120 (1966; Zbl 0143.33302)], it is proved that if a solution of a certain parabolic differential inequality satisfies Dirichlet conditions on the boundary of its domain, and if it decays in time with greater than exponential rapidity ...
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Averaging of Higher-Order Parabolic Equations with Periodic Coefficients

Contemporary Mathematics. Fundamental Directions, 2021
In L2(Rd;Cn), we consider a wide class of matrix elliptic operators A of order 2p (where p2) with periodic rapidly oscillating coefficients (depending on x/). Here 0 is a small parameter. We study the behavior of the operator exponent e-A for 0 and small .
A. A. Miloslova, T. A. Suslina
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A Perturbation Series for Cauchy's Problem for Higher-Order Abstract Parabolic Equations [PDF]

Proceedings of the National Academy of Sciences, 1970
The application of Phillips' perturbation theorem to Cauchy's problem for higher-order parabolic equations is justified by an argument from the theory of Fourier transforms of entire functions.
Donaldson, J. A., Hersh, R.
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Higher order nonlinear degenerate parabolic equations

Journal of Differential Equations, 1990
The paper deals with a few existence and positivity results for higher order, possibly degenerate, nonlinear parabolic equations. The equations under investigation are of the type \[ \frac{du}{dt}+\frac{\partial}{\partial \kappa}(f(u)\frac{\partial^{2m+1}u}{\partial \kappa^{2m+1}})=0 \] where \(f(u)=| u|^ m\) \(f_ 0(u)\) with \(n\geq 1\) and \(f_ 0(u ...
Bernis, Francisco, Friedman, Avner
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