Results 1 to 10 of about 14,488 (245)

A semilinear parabolic Volterra integrodifferential equation

Journal of Differential Equations, 1988
The authors study the existence of solutions of the equation \[ u'(t)+A(t)u(t)=\int^{t}_{t_ 0}a(t,s)g(s,u(s))ds+f(t,u(t)),\quad t\geq t_ 0,\quad u(t_ 0)=u_ 0, \] in a Banach space X. Here -A(t) is the generator of an analytic semigroup and the nonlinear operator g(t,\(\cdot)\) is Lipschitz continuous on the domain of A(0) in the graph norm.
Heard, Melvin L., Rankin, Samuel M.
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Existence and continuity of global attractors for a degenerate semilinear parabolic equation

Electronic Journal of Differential Equations, 2009
In this article, we study the existence and the upper semicontinuity with respect to the nonlinearity and the shape of the domain of global attractors for a semilinear degenerate parabolic equation involving the Grushin operator.
Cung The Anh, Tran Dinh Ke
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On the well-posedness of a class of McKean Feynman-Kac equations

, 2019
We analyze the well-posedness of a so called McKean Feynman-Kac Equation (MFKE), which is a McKean type equation with a Feynman-Kac perturbation. We provide in particular weak and strong existence conditions as well as pathwise uniqueness conditions ...
Lieber, Jonas, Oudjane, Nadia, Russo, Francesco   +2 more
core  

Semilinear heat equations and parabolic variational inequalities on graphs [PDF]

, 2021
Yong Lin, Yuanyuan Xie
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An abstract approximate controllability result and applications to elliptic and parabolic systems with dynamic boundary conditions

Electronic Journal of Differential Equations, 2001
In this paper we prove an approximate controllability result for an abstract semilinear evolution equation in a Hilbert space and we obtain as consequences the approximate controllability for some classes of elliptic and parabolic problems subjected to ...
Ioan Bejenaru, Jesus Ildefonso Diaz, Ioan I. Vrabie   +2 more
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Global Existence and Uniform Energy Decay Rates for the Semilinear Parabolic Equation with a Memory Term and Mixed Boundary Condition

Abstract and Applied Analysis, 2013
This work is concerned with a mixed boundary value problem for the semilinear parabolic equation with a memory term and generalized Lewis functions which depends on both spacial variable and time.
Zhong Bo Fang, Liru Qiu
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Removable singularities of semilinear parabolic equations

Advances in Differential Equations, 2010
We prove that the parabolic equation $$f_t=\Delta f+F(x,f,\nabla f,t), $$ in $(\mathbb R^m\setminus\{0\})\times(0,T)$, $m\ge 3$, has removable singularities at $\{0\}\times (0,T)$ if $\|f\|_{L^{\infty}(\mathbb{R}^m\setminus\{0\}\times (0,T))}
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Stationary solutions, blow up and convergence to stationary solutions for semilinear parabolic equations with nonlinear boundary conditions [PDF]

, 1991
Michel Chipot, Марек Фила, Pavol Quíttner   +2 more
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Global existence of solutions to one-phase Stefan problems for semilinear parabolic equations [PDF]

, 1998
Toyohiko Aiki, Hitoshi Imai
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Regularity and Exponential Growth of Pullback Attractors for Semilinear Parabolic Equations Involving the Grushin Operator

Abstract and Applied Analysis, 2012
Considered here is the first initial boundary value problem for a semilinear degenerate parabolic equation involving the Grushin operator in a bounded domain Ω.
Nguyen Dinh Binh
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