In Abstract Algebraic Logic the general study of propositional non-classical logics has been traditionally based on the abstraction of the Lindenbaum-Tarski process. In this kind of process one considers the Leibniz relation of indiscernible, i.e. logically equivalent, formulae. Such approach has resulted in a classification of logics partly based on generalizations of equivalence connectives: ...

In this paper we study the Cauchy problem for the semilinear heat and Schrödinger equations, with the nonlinear term f(u) = λ|u|αu. We show that low regularity of f (i.e., α > 0 but small) limits the regularity of any possible solution for a certain class of smooth initial data. We employ two different methods, which yield two different types of results. On the one hand, we consider the semilin...

In this paper, we prove that for a semilinear wave equation with source terms, the energy decays exponentially as time approaches infinity. For this end we use the the multiplier method.

We obtain maximum principles for solutions of some general fourth order elliptic equations by modifying an auxiliary function introduced by L.E. Payne. We give a brief application of these maximum principles by deducing apriori bounds on a certain quantity of interest.

A semilinear elliptic boundary-value problem on bounded multiconnected domains is studied. The authors prove that under suitable conditions, the problem may have no solutions in certain cases and many have one or two nonnegative solutions in some other cases. The radial solutions were also studied in annular domains.

We show local existence of solutions to the initial boundary value problem corresponding to a semilinear wave equation with interior damping and source terms. The difficulty in dealing with these two competitive forces comes from the fact that the source term is not a locally Lipschitz function from H1(Ω) into L2(Ω) as typically assumed in the literature. The strategy behind the proof is based ...

In this paper we show local existence of solutions to the initial boundary value problem corresponding to a semilinear wave equation with interior damping and source terms. The difficulty in dealing with these two competitive forces comes from the fact that the source term is not a locally Lipschitz function from H1(Ω) into L2(Ω) as typically assumed in the literature. The strategy behind the p...

<p style='text-indent:20px;'>In present paper, we deal with the behavior of a solution beyond occurrence wave breaking for modified periodic Coupled Camassa-Holm system. By introducing new set independent and dependent variables, which resolve all singularities due to possible breaking, this evolution system is rewritten as closed semilinear The local existence obtained fixed points contr...