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PARABOLIC EQUATIONS WITH NONLINEAR SINGULARITIES

, 2009
Martínez-Aparicio, Pedro J., Petitta, Francesco   +1 more
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A Nonlinear Parabolic Equation with Noise

Potential Analysis, 2000
The authors consider the semilinear stochastic parabolic partial differential equation (PDE, in short) with multiplicative white noise \[ \partial_t \varphi+ \sum^d_{k=1} \partial_k\bigl(f(t,x, \varphi(t,x) \bigr)= \nu\sum^d_{k=1} \partial^2_{x_k} \varphi+\sigma (t)\varphi(t,x)\dot W_t, \quad (t,x) \in[0,T] \times\mathbb{R}^n, \] where the stochastic ...
Benth, Fred Espen, Gjessing, Håkon K.
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STABILIZATION OF NONLINEAR PARABOLIC EQUATIONS

IFAC Proceedings Volumes, 1983
Abstract We are concerned with the possibility of constructing implementable feedback control laws to stabilize ů + Au = f(u), primarily through the boundary conditions. Semigroup methods are employed to reduce the semi- linear problem to a linear one, to show stabilizability of certain parabolic problems by feedback and, finally, to show for the one-
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Nonlinear Degenerate Parabolic Equations

Acta Mathematica Hungarica, 1997
The author proves the existence of weak solutions of the nonlinear degenerate parabolic initial-boundary value problem \[ {{\partial u}\over{\partial t}} - \sum_{i=1}^N D_iA_i(x,t,u,Du) + A_0(x,t,u,Du) = f(x,t)\quad\text{ in }\Omega\times(0,T), \] \[ u(x,0) = u_0(x)\quad \hbox{ in }\Omega, \] in the space \(L^p(0,T,W^{1,p}_0(v,\Omega))\), where ...
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Nonlinear Parabolic Equations

1985
In this chapter we wish to consider the nonlinear parabolic equation $$ \begin{gathered} {{u}_{t}} - {{u}_{{xx}}} = g(u) \hfill \\ u(0, t) = u(1,t) = 0 \hfill \\ \mathop{{\lim }}\limits_{{t \to 0}} u(x,t) = f(x) \hfill \\ \end{gathered} $$ (1) We wish to establish an analogue of the classical PoincareLyapunov theorem:If \(g\left( u \right ...
Richard Bellman, George Adomian
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Nonlinear Degenerate Parabolic Equations with a Singular Nonlinearity

Acta Applicandae Mathematicae
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Hichem Khelifi, Fares Mokhtari
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On the Solutions of the Coupled Nonlinear Parabolic Equations

Journal of Partial Differential Equations, 1996
Summary: By means of the fixed point technique and integral estimation method, we study the solutions of a periodic boundary value problem and an initial value problem for coupled nonlinear parabolic equations. The existence of global classical solutions to the mentioned problems is shown.
Shen, Longjun, Zhang, Linghai
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Parabolic equations with double variable nonlinearities

Mathematics and Computers in Simulation, 2011
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Stanislav N. Antontsev, Sergey Shmarev
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On the oscillations of solutions of nonlinear parabolic equations

Applied Mathematics and Computation, 2003
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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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