Results 11 to 20 of about 6,797 (118)

A note on lifespan estimates for higher‐order parabolic equations

Bulletin of the London Mathematical Society
Abstract We investigate the lifespan of solutions to the higher‐order semilinear parabolic equation  with initial data . We focus on the precise asymptotic behavior of the lifespan of nontrivial solutions.
Nurdaulet N. Tobakhanov, Berikbol T. Torebek   +1 more
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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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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.
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A Property of Weak Solutions for Some Parabolic Equations of Higher Order [PDF]

Nagoya Mathematical Journal, 1967
Recently Aronson [1] proved the uniqueness property of weak solutions of the initial boundary value problem for second order parabolic equations with discontinuous coefficients. An analogous result to Aronson’s was proved by Kuroda M in the case of some parabolic equations of higher order, where the method due to Aronson [2] plays an essential role. In
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Analysis of higher order difference method for a pseudo-parabolic equation with delay [PDF]

Miskolc Mathematical Notes, 2019
In this paper, the author considers the one dimensional initial-boundary problem for a pseudo-parabolic equation with time delay in second spatial derivative. To solve this problem numerically, the author constructs higher order difference method and obtain the error estimate for its solution.
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On Boundary Value Problems for Parabolic Equations of Higher Order in Time

Journal of Differential Equations, 1996
This paper is concerned with the initial-boundary value problem for the parabolic equations: \[ {\mathcal A}(t, x, \partial_t, \partial_x) u= f\quad\text{in } ]0, T]\times \Omega, \] \[ {\mathcal B}_\mu(t, x, \partial_t, \partial_x) u= g_\mu,\;\mu= 1,\dots, m,\text{ on } ]0, T]\times \partial \Omega, \] \[ u(0, x)= u_0(x),\dots, \partial^{\ell- 1}_t u ...
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Evolution operators for higher order abstract parabolic equations [PDF]

Czechoslovak Mathematical Journal, 1986
The author shows the existence of an evolution operator for a higher order abstract parabolic equation with variable coefficients. The techniques employed are similar to Tanabe's method [\textit{H. Tanabe}, Osaka Math. J. 12, 363-376 (1960; Zbl 0098.313)].
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Local solvability of higher order semilinear parabolic equations

Hokkaido Mathematical Journal, 1992
In this paper is considered the parabolic equation \(u_ t = - Pu + f(t,x,d^ mu)\) in \(D^ T\) with initial-boundary conditions \(u(0,x) = u_ 0 (x)\) in \(G\) \(B_ 0u = B_ 1u = \cdots = B_{m - 1} u = 0\) on \(\partial G\), where \(Pu = \sum_{| \alpha |, | \beta | \leq m} ( - 1)^{| \beta |} D^ \beta (a_{\alpha, \beta} (x)D^ \alpha u)\), \(m > 1\), \(G ...
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On the Dirichlet problem for certain higher order parabolic equations [PDF]

Pacific Journal of Mathematics, 1960
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Asymptotic analysis of higher order parabolic equations

Asymptotic analysis of higher order parabolic equations
博士学位論文 (Thesis(doctor))
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