Journals and Conference ProceedingsThe Journals and Conference Proceedings Collection includes publications reviewed and published by members of the university community and proceedings from conferences hosted by, or sponsored by, Texas State University.https://digital.library.txstate.edu/handle/10877/1362020-01-23T14:02:03Z2020-01-23T14:02:03ZBilinear Spatial Control of the Velocity Term in a Kirchhoff Plate EquationBradley, Mary ElizabethLenhart, Suzannehttps://digital.library.txstate.edu/handle/10877/91792020-01-14T17:17:23Z2001-05-01T00:00:00ZBilinear Spatial Control of the Velocity Term in a Kirchhoff Plate Equation
Bradley, Mary Elizabeth; Lenhart, Suzanne
We consider a bilinear optimal control problem with the state equation being a Kirchhoff plate equation. The control is a function of the spatial variables and acts as a multiplier of the velocity term. The unique optimal control, driving the state solution close to a desired evolution function, is characterized in terms of the solution of the optimality system.
2001-05-01T00:00:00ZOn the Solvability of Nonlocal Pluriparabolic ProblemsBouziani, Abdelfatahhttps://digital.library.txstate.edu/handle/10877/91782020-01-14T17:05:42Z2001-03-26T00:00:00ZOn the Solvability of Nonlocal Pluriparabolic Problems
Bouziani, Abdelfatah
The aim of this paper is to prove existence, uniqueness, and continuous dependence upon the data of solutions to mixed problems for pluriparabolic equations with nonlocal boundary conditions. The proofs are based on a priori estimates established in non-classical function spaces and on the density of the range of the operator generated by the studied problems.
2001-03-26T00:00:00ZPeriodic Solutions for a Class of Non-coercive Hamiltonian SystemsBoughariou, Morchedhttps://digital.library.txstate.edu/handle/10877/91682020-01-09T17:49:25Z2001-05-28T00:00:00ZPeriodic Solutions for a Class of Non-coercive Hamiltonian Systems
Boughariou, Morched
<p>We prove the existence of non-constant <i>T</i>-periodic orbits of the Hamiltonian system</p>
<p>q̇ = Hp(t,p(t), q(t))</p>
<p>ṗ = -Hq(t,p(t), q(t)).</p>
<p>where <i>H</i> is a <i>T</i>-periodic function in <i>t</i>, non-convex and non-coercive in (<i>p,q</i>), and has the form <i>H</i>(<i>t,p,q</i>) ∽ |q|α (|p|β - 1) with α > β > 1.</p>
2001-05-28T00:00:00ZSolutions of Nonlinear Parabolic Equations Without Growth Restrictions on the DataBoccardo, LucioGallouet, ThierryVazquez, Juan Luishttps://digital.library.txstate.edu/handle/10877/91672020-01-09T16:51:09Z2001-09-12T00:00:00ZSolutions of Nonlinear Parabolic Equations Without Growth Restrictions on the Data
Boccardo, Lucio; Gallouet, Thierry; Vazquez, Juan Luis
<p>The purpose of this paper is to prove the existence of solutions for certain types of nonlinear parabolic partial differential equations posed in the whole space, when the data are assumed to be merely locally integrable functions, without any control of their behaviour at infinity. A simple representative example of such an equation is</p>
<p>ut - Δu + |u|s-1 u = ƒ,</p>
<p>which admits a unique globally defined weak solution u(x,t) if the initial function u(x,0) is a locally integrable function of x ∈ ℝN and t ∈ [0,T] whenever the exponent <i>s</i> is larger than 1. The results extend to parabolic equations. They have no equivalent for linear or sub-linear zero-order nonlinearities.
2001-09-12T00:00:00Z