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Global Regularity of Solutions of Nonlinear Second Order Elliptic and Parabolic Differential Equations.

Gary M. Liebermann (1986)

Mathematische Zeitschrift

Global regularity of the Navier-Stokes equation on thin three-dimensional domains with periodic boundary conditions.

Montgomery-Smith, Stephen (1999)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Global Schauder estimates for a class of degenerate Kolmogorov equations

Enrico Priola (2009)

Studia Mathematica

We consider a class of possibly degenerate second order elliptic operators on ℝⁿ. This class includes hypoelliptic Ornstein-Uhlenbeck type operators having an additional first order term with unbounded coefficients. We establish global Schauder estimates in Hölder spaces both for elliptic equations and for parabolic Cauchy problems involving . The Hölder spaces in question are defined with respect to a possibly non-Euclidean metric related to the operator . Schauder estimates are deduced by sharp...

Global smooth solutions to a class of semilinear wave equations with strong nonlinearities.

Harmut Pecher (1990)

Manuscripta mathematica

Global solution for the Kadomtsev-Petviashvili equation (KPII) in anisotropic Sobolev spaces of negative indices.

Isaza J., Pedro, Mejía L., Jorge (2003)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Global Solution of the System of Wave and Klein-Gordon Equations.

Vladimir Georgiev (1990)

Mathematische Zeitschrift

Global solutions and exponential decay for a nonlinear coupled system of beam equations of Kirchhoff type with memory in a domain with moving boundary.

Santos, M.L., Soares, U.R. (2007)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

Global solutions and finite time blow up for damped semilinear wave equations

Filippo Gazzola, Marco Squassina (2006)

Annales de l'I.H.P. Analyse non linéaire

Global solutions and quenching to a class of quasilinear parabolic equations.

Bei Hu, Hong-Ming Yin (1994)

Forum mathematicum

Global solutions for a nonlinear hyperbolic equation with boundary memory source term.

Sun, Fuqin, Wang, Mingxin (2006)

Journal of Inequalities and Applications [electronic only]

Global solutions for a nonlinear wave equation with the $p$ -Laplacian operator.

Gao, Hongjun, Ma, To Fu (1999)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

Global solutions of multidimensional approximate Navier-Stokes equations of a viscous gas.

Lukina, E. V. (2003)

Sibirskij Matematicheskij Zhurnal

Global solutions of nonlinear parabolic equations

Matania Ben-Artzi (1992)

Journées équations aux dérivées partielles

Global solutions to a class fo strongly coupled parabolic systems.

Michael Wiegner (1992)

Mathematische Annalen

Global solutions to some nonlinear dissipative mildly degenerate Kirchhoff equations.

Ghisi, Marina (2003)

Portugaliae Mathematica. Nova Série

Global solvability in the parabolic-elliptic chemotaxis system with singular sensitivity and logistic source

Xiangdong Zhao (2024)

Czechoslovak Mathematical Journal

We study the chemotaxis system with singular sensitivity and logistic-type source: $u_{t} = Δ u - χ \nabla \cdot (u \nabla v / v) + r u - μ u^{k}$ , $0 = Δ v - v + u$ under the non-flux boundary conditions in a smooth bounded domain $Ω \subset ℝ^{n}$ , $χ, r, μ > 0$ , $k > 1$ and $n \geq 1$ . It is shown with $k \in (1, 2)$ that the system possesses a global generalized solution for $n \geq 2$ which is bounded when $χ > 0$ is suitably small related to $r > 0$ and the initial datum is properly small, and a global bounded classical solution for $n = 1$ .

Global sovability for the degenerate Krichhoff equation with real anlytic data.

P. D'Ancona, S. Spagnolo (1992)

Inventiones mathematicae

Global stability of travelling fronts for a damped wave equation with bistable nonlinearity

Thierry Gallay, Romain Joly (2009)

Annales scientifiques de l'École Normale Supérieure

We consider the damped wave equation $α u_{t t} + u_{t} = u_{x x} - V^{'} (u)$ on the whole real line, where $V$ is a bistable potential. This equation has travelling front solutions of the form $u (x, t) = h (x - s t)$ which describe a moving interface between two different steady states of the system, one of which being the global minimum of $V$ . We show that, if the initial data are sufficiently close to the profile of a front for large $| x |$ , the solution of the damped wave equation converges uniformly on $ℝ$ to a travelling front as $t \to + \infty$ . The proof of this global stability...

Global Strichartz estimates for variable coefficient second order hyperbolic operators

Daniel Tataru (1999/2000)

Séminaire Équations aux dérivées partielles

Global strong solution and its decay properties for the Navier-Stokes equations in three dimensional domains with non-compact boundaries.

Hideo Kozono, Takayoshi Ogawa (1994)

Mathematische Zeitschrift

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