Results 181 to 190 of about 234,656 (222)

On higher order parabolic functional differential equations

Periodica Mathematica Hungarica, 1995
The 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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Schauder-type estimates for higher-order parabolic SPDEs

Journal of evolution equations (Printed ed.), 2019
In this paper, we consider the Cauchy problem for 2 m -order stochastic partial differential equations of parabolic type in a class of stochastic Hölder spaces. The Hölder estimates of solutions and their spatial derivatives up to order 2 m are obtained,
Yuxing Wang, Kai Du
semanticscholar   +1 more source

Higher-order operator splitting methods for deterministic parabolic equations

International Journal of Computer Mathematics, 2007
The Sheng-Suzuki theorem states that all exponential operator splitting methods of order greater than 2 must contain negative time integration. There have been claims in the literature that higher-order splitting methods for deterministic parabolic equations are unstable due to this fact.
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Dissipative mechanism of a semilinear higher order parabolic equation in

Nonlinear Analysis: Theory, Methods & Applications, 2012
It is known that the concept of dissipativeness is fundamental for understanding the asymptotic behavior of solutions to evolutionary problems. In this paper we investigate the dissipative mechanism for some semilinear fourth-order parabolic equations in the spaces of Bessel potentials and discuss some weak conditions that lead to the existence of a ...
Jan W. Cholewa, Anibal Rodriguez-Bernal
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ON THE EXISTENCE OF STRONG SOLUTIONS OF HIGHER ORDER QUASILINEAR PARABOLIC EQUATIONS

UZBEK MATHEMATICAL JOURNAL
We consider boundary value problems for quasilinear parabolic equations with a main quasilinear elliptic operator of order 2b ≥ 2 in Sobolev space W2b,1 p (QT ).
Amanova, N. R., Khalilov, V. S.
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Phase space path integral on torus for the fundamental solution of higher-order parabolic equations

, 2020
Naoto Kumano-go, K. Uchida
semanticscholar   +1 more source

Initial value problem of a higher order parabolic equation

Periodica Mathematica Hungarica, 1988
In the present work the initial value problem of the equation \[ D^ k_ t u=\sum^{k}_{j=1}a_ jD_ t^{k-j}(-1)^{m+1} \nabla^{2m} u+\sum^{k-1}_{j=0}\Lambda_ j(t)D^ j_ t u \] where \((A_ j(t)\), \(j=0,1,...,k-1\), \(0\leq t\leq T)\) is a family of bounded linear operators defined on \(C(R_ n)\), the space of all continuous functions defined on \(R_ n\) with
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Higher order parabolic approximations of the reduced wave equation

Journal of Sound and Vibration, 1986
Asymptotic solutions of order \(k^{-n}\) are developd for the reduced wave equation. Here k is a dimensionless wave number and n is the arbitrary order of the approximation. These approximations are an extension of geometric acoustics theory and provide corrections to that theory in the form of multiplicative functions which satisfy parabolic partial ...
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Inverse Problems for Higher Order Parabolic Equations

1998
Inverse problems for higher order parabolic equations.
KAMYNIN V. L., SAROLDI M., FRANCINI, ELISA   +2 more
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Applications and time‐domain solution of higher‐order parabolic equations in underwater acoustics

, 1989
M. D. Collins
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