Results 171 to 180 of about 341,593 (214)

Nonlocal and abstract parabolic equations and their applications

Banach Center Publications, 2009
Piotr Bogusław Mucha, M. Niezgodka, P. Rybka   +2 more
semanticscholar   +2 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.
openaire   +1 more source

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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Stability results for backward time-fractional parabolic equations

Inverse Problems, 2019
Optimal order stability estimates of Hölder type for the backward Caputo time-fractional abstract parabolic equations are obtained. This ill-posed problem is regularized by a non-local boundary value problem method with a priori and a posteriori ...
Dinh Nho Hào, Jijun Liu, Nguyen Van Duc, Nguyen Van Thang   +3 more
semanticscholar   +1 more source

Inverse problems for stochastic parabolic equations with additive noise

, 2020
In this paper, we study two inverse problems for stochastic parabolic equations with additive noise. One is to determinate the history of a stochastic heat process and the random heat source simultaneously by the observation at the final time 𝑇. For this
Ganghua Yuan
semanticscholar   +1 more source

Quasilinear Abstract Parabolic Evolution Equations with Applications

2002
We are concerned with the Cauchy problem of a quasilinear parabolic evolution equation $$ \left\{ {\begin{array}{*{20}{c}} {\frac{{dU}}{{dt}} + A\left( U \right)U = F\left( U \right),0 < t \leqslant T,} \\ {U(0) = {U_{0}}} \\ \end{array} } \right. $$
openaire   +1 more source

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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Abstract singular parabolic equations

Communications in Partial Differential Equations, 1982
Jeff E. Lewis, Cesare Parenti
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A unified approach to abstract linear nonautonomous parabolic equations

1987
The paper can be considered as a review, in which - on the basis of certain assumptions - a unified approach to abstract linear nonautonomous parabolic equations is proposed. In particular, the linear parabolic Cauchy problem \[ (1)\quad u'(t)-A(t)u(t)=f(t),\quad t\in [0,T],\quad u'(0)=x \] is studied in a Banach space E, with \(x\in E\) and f:[0,T ...
ACQUISTAPACE, PAOLO, TERRENI B.
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