Results 171 to 180 of about 233,661 (218)

Inequalities for Nonlocal Parabolic and Higher Order Elliptic Equations

SIAM Review, 1967
Abstract : A general method is illustrated for obtaining L(2) bounds for nonlocal problems by using known bounds for corresponding strictly differential problems. The method is applied to obtain L(2) and pointwise bounds for perturbed second order parabolic and fourth order elliptic problems. (Author)
Gustafson, K., Sigillito, V.
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Note on a higher order pseudo‐parabolic equation with variable exponents

Mathematical Methods in the Applied Sciences, 2023
In 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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Nonlinear vibration and dynamic buckling responses of stiffened functionally graded graphene‐reinforced cylindrical, parabolic, and sinusoid panels using the higher‐order shear deformation theory

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 2023
The nonlinear vibration and dynamic responses of functionally graded graphene‐reinforced composite (FG‐GRC) laminated cylindrical, parabolic, and sinusoid panels stiffened by FG‐GRC stiffeners in the uniformly distributed temperature variation are ...
T. Q. Minh, V. H. Nam, Vu Minh Duc, Vu Tho Hung, Le Ngoc Ly, Nguyen Thi Hong Phuong   +5 more
semanticscholar   +1 more source

Parabolicity of a Class of Higher-Order Abstract Differential Equations

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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Self-Similar Blow-Up in Higher-Order Semilinear Parabolic Equations

SIAM Journal on Applied Mathematics, 2004
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Budd, C. J., Galaktionov, V. A., Williams, J. F.   +2 more
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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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On Doubly Degenerate Quasilinear Parabolic Equations of Higher Order

Acta Mathematica Sinica, English Series, 2004
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Extinction of solutions of semilinear higher order parabolic equations with degenerate absorption potential

, 2009
We study the first vanishing time for solutions of the Cauchy–Dirichlet problem for the 2m-order (m ≥ 1) semilinear parabolic equation $${u_t + Lu + a(x) |u|^{q-1}u=0,\,0 < q < 1}$$ with a(x) ≥ 0 bounded in the bounded domain $${\Omega \subset \mathbb R ...
Y. Belaud, A. Shishkov
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On degenerate quasilinear parabolic equations of higher order

Periodica Mathematica Hungarica, 1996
zbMATH 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, 1983
A 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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