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Análise e Equações com Derivadas Parciais

Editor Convidado: Lisa Santos Autores & Artigos Assis Azevedo, Fernando Miranda, Lisa Santos, "Multiplicador de Lagrange num problema com restrição não constante no gradiente" Hermenegildo Borges de Oliveira, "Resultados de existência de soluções fracas para fluidos viscosos incompressíveis" Nabil Bedjaoui, Joaquim M. C. Correia, "A note on nonlinear KdV-type equations" N.V. Chemetov, F. Cipriano, "Proble...

Stationary quasivariational inequalities with gradient constraint and nonhomoge...

Publicado em "From particle systems to partial differential equations. Part 2. (Springer proceedings in mathematics & statistics, vol. 75). ISBN 978-3-642-54270-1 ; We study existence of solution of stationary uasivariational inequalities with gradient constraint and nonhomogeneous boundary condition of Neumann or Dirichlet type. Through two different approaches, one making use of a fixed point theorem and th...

Variational and quasivariational inequalities with first order constraint

We study the existence of solutions of stationary variational and quasivariational inequalities with curl constraint, Neumann type boundary condition and a p-curl type operator. These problems are studied in bounded, not necessarily simply connected domains, with a special geometry, and the functional framework is the space of divergence-free functions with curl in $\boldsymbol L^p$ and null tangential or no...

On a p-curl system arising in electromagnetism

We prove existence of solution of a $p$-curl type evolutionary system arising in electromagnetism with a power nonlinearity of order $p$, $1<p<\infty$, assuming natural tangential boundary conditions. We consider also the asymptotic behaviour in the power obtaining, when $p$ tends to infinity, a variational inequality with a curl constraint. We also discuss the existence, uniqueness and continuous dependence o...

A nonlinear hyperbolic Maxwell system using measure-valued functions

We consider a modified antenna's problem with power-type constitutive laws. This consists in a new nonlinear hyperbolic system that extends a Duvaut-Lions model. Using the Galerkin approximation, properties of the natural functional spaces, and exploring the $L^p$-$L^{p'}$ duality, we prove the existence of solutions, in a generalized sense, passing to the limit in a family of approximated problems and using me...

Quasivariational solutions for first order quasilinear equations with gradient ...

We prove the existence of solutions for an evolution quasi-variational inequality with a first order quasilinear operator and a variable convex set which is characterized by a constraint on the absolute value of the gradient that depends on the solution itself. The only required assumption on the nonlinearity of this constraint is its continuity and positivity. The method relies on an appropriate parabolic regu...

A class of electromagnetic p-curl systems : blow-up and finite time extinction

We study a class of $p$-curl systems arising in electromagnetism, for $\frac65 < p < \infty$, with nonlinear source or sink terms. Denoting by $\boldsymbol h$ the magnetic field, the source terms considered are of the form $\boldsymbol h\left(\int_\Omega; \boldsymbol h; ^2\right)^{\frac{\sigma-2}{2}}$, with $\sigma\geq1$. Existence of local or global solutions is proved depending on values of $\sigma$ and $p$....

Multiplicador de Lagrange num problema com restrição não constante no gradiente

Prova-se a existência de solução, num sentido generalizado, de um problema com um multiplicador de Lagrange, para uma restrição arbitrária no gradiente e condição de Dirichlet homogénea na fronteira. Prova-se ainda a equivalência deste problema com a correspondente inequação variacional elíptica. A abordagem utilizada para provar o resultado de existência baseia-se na utilização de soluções de uma família aprox...

A diffusion problem with gradient constraint depending on the temperature

We consider a system of a variational inequality with gradient constraint depending on the temperature, coupled with the heat equation. We prove existence of solution of this system by approximating it by a system of equations and using a fixed point argument.

Research seminar on history and epistemology of mathematics : proceedings