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Parabolic-Type Integrodifferential Equations
2011The study of many physical processes arising in science and engineering leads to the models of parabolic integrodifferential equations with different initial boundary conditions. These equations occur in several applications, such as in heat flow in materials with memory, control and optimization theories, reaction diffusion processes, epidemic models ...
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An Abstract Parabolic Volterra Integrodifferential Equation
SIAM Journal on Mathematical Analysis, 1982We 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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On a semilinear volterra integrodifferential equation
Israel Journal of Mathematics, 1980The Volterra integrodifferential equation $$\begin{array}{*{20}c} {u_t (t,x) + \smallint '_0 a(t - s)( - \Delta u(s,x) + f(x,u(s,x)))ds = h(t,x),,} \\ {t > 0,x \in \Omega \subset R^N ,} \\ \end{array} $$ together with boundary and initial conditions is considered.
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Asymptotic behavior of volterra integrodifferential equations
Acta Mathematicae Applicatae Sinica, 1997The asymptotic behavior and boundedness of the solution of the Volterra integrodifferential equation \[ x'(t)= A(t)x(t)+ \int_0^t C(t,s)x(s)ds+ \int_0^t G(t,s,x(s))ds+ f(t), \] where \(x\in\mathbb{R}^n\), \(A(t)\) and \(C(t,s)\) are continuous \(n\times n\) matrices, and \(f(t)\) is continuous \(n\)-vectors, is studied.
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Differential and Integrodifferential Equations
2012There are strong connections between the theory of integral equations and the theory of differential equations. Although there are many ways to illustrate, analyze, and interpret these connections, we can only discuss a few of them in this chapter.
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Integrodifferential Equation for Response Theory
Physical Review A, 1971The problem of response theory in statistical mechanics involves the determination of the density matrix $\ensuremath{\rho}$ from the Liouville equation and the subsequent computation of the response $r$ from this $\ensuremath{\rho}$. Projection techniques are applied to avoid the entire complicated problem of the full dynamics of $\ensuremath{\rho ...
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Linear stochastic integrodifferential equations
1989Pitman Research Notes in Mathematics Series, 190. This volume collects the contributions to the conference "Volterra Integrodifferential Equations in Banach Spaces and Applications" held in Trento (Italy) February 2-7, 1987.
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On degenerating integrodifferential equations
Siberian Mathematical Journal, 1973openaire +1 more source