Results 1 to 10 of about 233,641 (201)
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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Higher order linear parabolic equations [PDF]
, 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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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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On nonexistence of Baras--Goldstein type for higher-order parabolic equations with singular potentials [PDF]
, 2009 An analogy of nonexistence result by Baras and Goldstein (1984), for the heat equation with inverse singular potential, is proved for 2mth-order linear parabolic equations with Hardy-supercritical singular potentials.
Galaktionov, V. A., Kamotski, I. V.
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Higher-order boundary regularity estimates for nonlocal parabolic equations [PDF]
Calculus of Variations and Partial Differential Equations, 2018 We establish sharp higher-order H lder regularity estimates up to the boundary for solutions to equations of the form $\partial_t u-Lu=f(t,x)$ in $I\times $ where $I\subset\mathbb{R}$, $ \subset\mathbb{R}^n$ and $f$ is H lder continuous. The nonlocal operators $L$ considered are those arising in stochastic processes with jumps such as the ...
Ros Oton, Xavier +1 more
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Unique continuation through hyperplane for higher order parabolic and Schrödinger equations [PDF]
Communications in Partial Differential Equations, 2021 Consider the higher order parabolic operator $\partial_t+(- _x)^m$ and the higher order Schr dinger operator $i^{-1}\partial_t+(- _x)^m$ in $X=\{(t,x)\in\mathbb{R}^{1+n};~|t|0$, then the solutions vanish in $X$. Such results are global if $n>1$, and we also prove some relevant local results.
Tianxiao Huang
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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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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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Boundary value problems for higher order parabolic equations [PDF]
Transactions of the American Mathematical Society, 2000 We consider a constant coefficient parabolic equation of order 2 m 2m and establish the existence of solutions to the initial-Dirichlet problem in cylindrical domains. The lateral data is taken from spaces of Whitney arrays which essentially require that the normal derivatives up to order m −
Brown, Russell M., Hu, Wei
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