Smoothing for Nonlinear Parabolic Equations with Nonlinear Boundary Conditions
Journal of Mathematical Analysis and Applications, 1997 The authors are concerned with smoothing effects for a class of nonlinear partial differential equations of parabolic type. They extend some known properties of the solution in the linear case, to their nonlinear case. Such properties are: \(u_t(\cdot, t)\to 0\) as \(t\to \infty\) in the \(L^2\)-norm, and \(u(\cdot,t)\) is bounded on \((0,\infty ...
Goldstein, Gisèle Ruiz +1 more
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Blow-Up Phenomena for Nonlinear Reaction-Diffusion Equations under Nonlinear Boundary Conditions
Journal of Function Spaces, 2016 This paper deals with blow-up and global solutions of the following nonlinear reaction-diffusion equations under nonlinear boundary conditions: g(u)t=∇·au∇u+fu in Ω×0,T, ∂u/∂n=bx,u,t on ∂Ω×(0,T), u(x,0)=u0(x)>0, in Ω¯, where Ω⊂RN (N≥2) is a ...
Juntang Ding
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Constraint-preserving boundary treatment for a harmonic formulation of the Einstein equations [PDF]
, 2008 We present a set of well-posed constraint-preserving boundary conditions for a first-order in time, second-order in space, harmonic formulation of the Einstein equations.
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Parabolic Problems with Nonlinear Boundary Conditions and Critical Nonlinearities
Journal of Differential Equations, 1999 The authors study the nonlinear parabolic problem \[ \begin{gathered} \frac {\partial u}{\partial t} =\Delta u + f(u) \text{ in } \Omega\times(0,T), \\ \frac {\partial u}{\partial \nu} = g(u) \text{ on } \partial\Omega\times(0,T), \\ u(\cdot,0) = u_0 \text{ in } \Omega, \end{gathered} \] where \(\Omega \subset \mathbb R^N\) has unit outer normal \(\nu\)
Arrieta, José M +2 more
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Boundary element methods for potential problems with nonlinear boundary conditions [PDF]
Mathematics of Computation, 2000 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ganesh, M., Steinbach, O.
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Balanced Truncation Model Reduction of a Nonlinear Cable-Mass PDE System with Interior Damping
, 2018 We consider model order reduction of a nonlinear cable-mass system modeled by a 1D wave equation with interior damping and dynamic boundary conditions. The system is driven by a time dependent forcing input to a linear mass-spring system at one boundary.
Batten, Belinda A. +3 more
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Positive solutions of nonlinear fourth-order boundary-value problems with local and non-local boundary conditions [PDF]
, 2008 We establish new existence results for multiple positive solutions of fourth-order nonlinear equations which model deflections of an elastic beam. We consider the widely studied boundary conditions corresponding to clamped and hinged ends and many non ...
Franco, D., Infante, G., Webb, J.R.L.
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Quasilinear equations involving nonlinear Neumann boundary conditions
Differential and Integral Equations, 2012 26
Iturriaga, Leonelo +3 more
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Unsteady nonlinear panel method with mixed boundary conditions [PDF]
FME Transactions, 2021 A new panel method had been developed to account for unsteady nonlinear subsonic flow. Two boundary conditions were used to solve the potential flow about complex configurations of airplanes.
Hamid Ali Anmar
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Boundary Value Problems For Integrable Equations Compatible With The Symmetry Algebra [PDF]
, 1994 Boundary value problems for integrable nonlinear partial differential equations are considered from the symmetry point of view. Families of boundary conditions compatible with the Harry-Dym, KdV and MKdV equations and the Volterra chain are discussed. We
Burak Gürel +4 more
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