Results 11 to 20 of about 106 (80)

New Results About the Lambda Constant and Ground States of the 𝑊-Functional

Advanced Nonlinear Studies, 2020
In this paper, we study properties of the lambda constants and the existence of ground states of Perelman’s famous W-functional from a variational formulation. We have two kinds of results.
Ma Li
doaj   +1 more source

Nonanalytic solutions of the KdV equation

Abstract and Applied Analysis, Volume 2004, Issue 6, Page 453-460, 2004., 2004
We construct nonanalytic solutions to the initial value problem for the KdV equation with analytic initial data in both the periodic and the nonperiodic cases.
Peter Byers, A. Alexandrou Himonas
wiley   +1 more source

Which solutions of the third problem for the Poisson equation are bounded?

Abstract and Applied Analysis, Volume 2004, Issue 6, Page 501-510, 2004., 2004
This paper deals with the problem Δu = g on G and ∂u/∂n + uf = L on ∂G. Here, G ⊂ ℝm, m > 2, is a bounded domain with Lyapunov boundary, f is a bounded nonnegative function on the boundary of G, L is a bounded linear functional on W1,2(G) representable by a real measure μ on the boundary of G, and g ∈ L2(G)∩Lp(G), p > m/2.
Dagmar Medková
wiley   +1 more source

Coefficients of singularities of the biharmonic problem of Neumann type: case of the crack

International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 5, Page 305-313, 2003., 2003
This paper concerns the biharmonic problem of Neumann type in a sector V. We give a representation of the solution u of the problem in a form of a series u = ∑α∈ECα rα ϕα, and the functions ϕα are solutions of an auxiliary problem obtained by the separation of variables.
Wided Chikouche, Aissa Aibèche
wiley   +1 more source

Results on existence for generalized nD Navier-Stokes equations

Open Mathematics, 2019
In this paper we consider a class of nD Navier-Stokes equations of Kirchhoff type and prove the global existence of solutions by using a new approach introduced in [Jday R., Zennir Kh., Georgiev S.G., Existence and smoothness for new class of n ...
Zennir Khaled
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Notes on continuity result for conformable diffusion equation on the sphere: The linear case

Demonstratio Mathematica, 2022
In this article, we are interested in the linear conformable diffusion equation on the sphere. Our main goal is to establish some results on the continuity problem with respect to fractional order.
Nguyen Van Tien
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Integrodifferential equations with analytic semigroups

International Journal of Stochastic Analysis, Volume 16, Issue 2, Page 177-189, 2003., 2003
In this paper we study a class of integrodifferential equations considered in an arbitrary Banach space. Using the theory of analytic semigroups we establish the existence, uniqueness, regularity and continuation of solutions to these integrodifferential equations.
D. Bahuguna
wiley   +1 more source

On the strongly damped wave equation and the heat equation with mixed boundary conditions

Abstract and Applied Analysis, Volume 5, Issue 3, Page 175-189, 2000., 2000
We study two one‐dimensional equations: the strongly damped wave equation and the heat equation, both with mixed boundary conditions. We prove the existence of global strong solutions and the existence of compact global attractors for these equations in two different spaces.
Aloisio F. Neves
wiley   +1 more source

Weakly hyperbolic equations with time degeneracy in Sobolev spaces

Abstract and Applied Analysis, Volume 2, Issue 3-4, Page 239-256, 1997., 1997
The theory of nonlinear weakly hyperbolic equations was developed during the last decade in an astonishing way. Today we have a good overview about assumptions which guarantee local well posedness in spaces of smooth functions (C∞, Gevrey). But the situation is completely unclear in the case of Sobolev spaces.
Michael Reissig
wiley   +1 more source

Optimality of Serrin type extension criteria to the Navier-Stokes equations

Advances in Nonlinear Analysis, 2021
We prove that a strong solution u to the Navier-Stokes equations on (0, T) can be extended if either u ∈ Lθ(0, T; U˙∞,1/θ,∞−α$\begin{array}{} \displaystyle \dot{U}^{-\alpha}_{\infty,1/\theta,\infty} \end{array}$) for 2/θ + α = 1, 0 < α < 1 or u ∈ L2(0, T;
Farwig Reinhard, Kanamaru Ryo
doaj   +1 more source