1,721,054 research outputs found
Nonnegative controllability for a class of nonlinear degenerate parabolic equations with application to climate science
Full text linkWe consider a nonlinear degenerate reaction-di↵usion equation. First we prove that if the initial state is nonnegative, then the solution re- mains nonnegative for all time. Then we prove the approximate controllability between nonnegative states via multiplicative controls, this is done using the reaction coecient as control
Approximate multiplicative controllability for degenerate parabolic problems and regularity properties of elliptic and parabolic systems
No full textThis thesis consists of two parts, both related to the theory of parabolic equations and systems. The first part is devoted to control theory which studies the possibility of influencing the evolution of a given system by an external action called control. Here we address approximate controllability problems via multiplicative controls, motivated by our interest in some differential models for the study of climatology.
In the second part of the thesis we address regularity issues on the local differentiabil- ity and Ho ̈lder regularity for weak solutions of nonlinear systems in divergence form. In order to improve readability, the two parts have been organized as completely in- dependent chapters, with two separate introductions and bibliographies.
All the new results of this thesis have been presented at conferences and workshops, and most of them appeared or are to appear as research articles in international journals. Related directions for future research are also outlined in body of the work
Backward problems in time for fractional diffusion-wave equation
No full textIn this article, for a time-fractional diffusion-wave equation partial derivative(alpha)(t)u(x, t) = -Au(x, t), 0 < t < T with fractional order alpha is an element of (1, 2), we consider the backward problem in time: determine u(., t), 0 < t < T by u(., T) and partial differential partial derivative(t)u(., T). We prove that there exists a countably infinite set Lambda subset of (0, infinity) with a unique accumulation point 0 such that the backward problem is well-posed for T is not an element of Lambda
Approximate controllability for linear degenerate parabolic problems with bilinear control
No full textIn this work we study the global approximate multiplicative controllability for the linear degenerate parabolic Cauchy-Neumann problem
\left\{\begin{array}{l}
\displaystyle{v_t-(a(x) v_x)_x =\alpha (t,x)v\,\,\qquad \mbox{in} \qquad Q_T \,=\,(0,T)\times(-1,1) }\\ [2.5ex]
\displaystyle{a(x)v_x(t,x)|_{x=\pm 1} = 0\,\,\qquad\qquad\qquad\,\, t\in (0,T) }\\ [2.5ex]
\displaystyle{v(0,x)=v_0 (x) \,\qquad\qquad\qquad\qquad\quad\,\, x\in (-1,1)}~,
\end{array}\right.
with the bilinear control The problem is strongly degenerate in the sense that positive on is allowed to vanish at provided that a certain integrability
condition is fulfilled.
We will show that the above system can be steered in from any nonzero, nonnegative initial state into any neighborhood of any desirable nonnegative target-state by bilinear static controls.
Moreover, we extend the above result relaxing the sign constraint on
Well-posedness for a class of nonlinear degenerate parabolic equations
No full textIn this paper we obtain well-posedness for a class of semilinear weakly degenerate
reaction-diffusion systems with Robin boundary conditions. This result is obtained
through a Gagliardo-Nirenberg interpolation inequality and some embedding results for
weighted Sobolev spaces
Approximate controllability of degenerate parabolic equations governed by bilinear control arising in climatology
No full textControllabilità moltiplicativa approssimata di equazioni paraboliche degeneri con applicazioni alla climatologia
No full textApproximate multiplicative controllability for degenerate parabolic problems with Robin boundary conditions
No full textIn this work we study the global approximate multiplicative controllability for a weakly degenerate parabolic Cauchy-Robin problem. The problem is weakly degenerate in the sense that the diffusion coefficient is positive in the interior of the domain and is allowed to vanish at the boundary, provided the reciprocal of the diffusion coefficient is summable. In this paper, we will show that the above system can be steered, in the space of square-summable functions, from any nonzero, nonnegative initial state into any neighborhood of any desirable nonnegative target-state by bilinear static controls. Moreover, we extend the above result relaxing the sign constraint on the initial-state
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