Nonlinear boundary conditions - Open Access .click

Applied Mathematics and Computation, 2021
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Adriano A. Alcântara +4 more
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Boundary-value problems with nonlinear boundary conditions

Nonlinearity, 1988
The authors deal with a general boundary value problem of the type: \(x'=F(t,x),T(x)=y,y\in R^ n\) where \(F(t,x)=A(t)x+f(t,x)\) and T is a continuous but not necessarily linear operator. It is shown that under suitable conditions the problem has at least one solution. The proof relies on a fixed-point theorem for condensing maps.
ANICHINI, GIUSEPPE, CONTI, GIUSEPPE
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Nonlinear Degenerate Parabolic Equation with Nonlinear Boundary Condition

Acta Mathematica Sinica, English Series, 2005
The authors study the existence and nonexistence of global positive solutions to the following nonlinear parabolic equation with nonlinear boundary conditions \[ \begin{aligned} & (u^k)_t = \Delta_mu,\quad x \in\Omega, \quad t > 0,\\ & \nabla_m u\cdot\nu = u^{\alpha},\quad x\in \partial\Omega, \quad t > 0,\\ & u(x,0) = u_0(x),\quad x\in\bar\Omega, \end{
Sun, Wenjun, Wang, Shu
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analysis
mathematics
asymptotic behavior of solutions to pdes

nonlinear boundary condition
applied mathematics
existence

fos: mathematics
nonlinear boundary value problem
boundary value problem