Results 141 to 150 of about 113,647 (186)

Single-cell mass-density measurements using microchannel gradient centrifugation

Soller R, Augustsson P, Barnkob R.
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An Abstract Parabolic Volterra Integrodifferential Equation

SIAM Journal on Mathematical Analysis, 1982
We consider semilinear integrodifferential equations of the form \[ u'(t) + A(t)u(t) = \int_0^t {\left[ {a(t,s)g_0 (s,u(s)) + g_1 (t,s,u(s))} \right]ds + f_0 (t) + f_1 (t,u(t)),} \]\[ u(0) = u_0 . \] For each $t \geqq 0$, the operator $A(t)$ is assumed to be the negative generator of an analytic semigroup in a Banach space X.
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Dynamic theory of quasilinear parabolic equations—I. Abstract evolution equations

Nonlinear Analysis: Theory, Methods & Applications, 1988
The author studies the qualitative properties of the solutions v of an abstract ordinary differential equation of the form \[ (1)\quad v'+A(t,v)v=F(t,v), \] where A(t,v) is the infinitesimal generator of an analytic semigroup in a Banach space. Under suitable Hölder continuity assumptions on A and F, several properties of the solutions v of (1) are ...
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Moving Surfaces and Abstract Parabolic Evolution Equations

1999
It is the purpose of this paper to give a survey over some recent developments in the theory of classical solutions to elliptic and parabolic problems involving moving surfaces. Problems of this type do not satisfy a superposition principle for solutions and, hence, carry an inherent nonlinear structure. In fact, it turns out that most of the equations
Joachim Escher, Gieri Simonett
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Stabilization of Abstract Parabolic Equations

2019
In this chapter, we present a technique to design asymptotically exponentially stabilizing boundary proportional-type feedback controllers for nonlinear parabolic-like equations, namely equations for which their linear parts are generated by analytic \(C_0\)-semigroups.
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Quasilinear Abstract Parabolic Evolution Equations with Applications

2002
We are concerned with the Cauchy problem of a quasilinear parabolic evolution equation $$ \left\{ {\begin{array}{*{20}{c}} {\frac{{dU}}{{dt}} + A\left( U \right)U = F\left( U \right),0 < t \leqslant T,} \\ {U(0) = {U_{0}}} \\ \end{array} } \right. $$
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Hölder regularity for non-autonomous abstract parabolic equations

Israel Journal of Mathematics, 1982
This paper contains some existence and uniqueness results for the strict and classical solutionsu : [0,T] →E of the non-autonomous evolution equationu 1(t)=Λ(t)u(t)+f(t) in a Banach spaceE under the classical Tanabe-Sobolevski assumptions.
Da Prato, Giuseppe, Sinestrari, Eugenio
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Bounded solutions of linear periodic abstract parabolic equations

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1988
SynopsisWe study the asymptotic behaviour of the parabolic evolution operatorG(t,s) associated with a family of generators of analytic semigroups {A(t);t∊ ℝ} in general Banach space, under the periodicity assumptionA(t) =A(t+T). We find new maximal regularity results for the bounded solutions of abstract nonhomogeneous parabolic equations in unbounded ...
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On the evolution operator for abstract parabolic equations

Israel Journal of Mathematics, 1987
The initial value problem for the differential equation in Banach space X is considered: \[ (1)\quad u'(t)=A(t)u(t)+f(t),\quad t_ ...
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