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Symmetry-enforced topological Dirac semimetal for giant spin-orbit torque with ultralow power dissipation. [PDF]

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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 ...
Herbert Amann
exaly   +3 more sources

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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A JUSTIFICATION OF THE AVERAGING METHOD FOR ABSTRACT PARABOLIC EQUATIONS

Mathematics of the USSR-Sbornik, 1970
In this paper the method of averaging of N.N. Bogoljubov is applied to abstract parabolic equations of the form (1)where is a linear, in general unbounded, operator generating an analytic semigroup, and is an operator subordinate to , in general a nonlinear map, possessing the mean Other conditions on the mapping are formulated in terms of the theory ...
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Parabolicity of a Class of Higher-Order Abstract Differential Equations

Proceedings of the American Mathematical Society, 1994
Summary: Let \(E\) be a complex Banach space, \(c_ i\in \mathbb{C}\) \((1\leq i\leq n- 1)\), and \(A\) be a nonnegative operator in \(E\). We discuss the parabolicity of the higher-order abstract differential equations \[ u^{(n)}(t)+ \sum^{n- 1}_{i= 1} c_ i A^{k_ i} u^{(n- i)}(t)+ Au(t)= 0\leqno{(*)} \] and some perturbation cases of \((*)\).
Xio, Tijun, Liang, Jin
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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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