Explicit solution of a class of higher-order abstract Cauchy problems

Explicit ABS Solution of a Class of Linear Inequality Systems and LP Problems

Higher Order Cauchy Problems in Bounded Domains

Abstract. We study solutions of a class of higher order partial differential equations in bounded domains. These partial differential equations appeared first time in the papers of Baeumer, Meerschaert and Nane [10] and Meerschaert, Nane and Vellaisamy [31], and Nane [36]. We express the solutions by subordinating a killed Markov process by a hitting time of a stable subordinator of index 0 < β...

On boundary value problems of higher order abstract fractional integro-differential equations

The aim of this paper is to establish the existence of solutions of boundary value problems of nonlinear fractional integro-differential equations involving Caputo fractional derivative by using the techniques such as fractional calculus, H"{o}lder inequality, Krasnoselskii's fixed point theorem and nonlinear alternative of Leray-Schauder type. Examples are exhibited to illustrate the main resu...

UNIQUENESS OF SOLUTION FOR A CLASS OF STEFAN PROBLEMS

This paper deals with a theoretical mathematical analysis of one-dimensional solidification problem, in which kinetic undercooling is incorporated into the This temperature condition at the interface. A model problem with nonlinear kinetic law is considered. We prove a local result intimate for the uniqueness of solution of the corresponding free boundary problem.

Approximation Theorems for the Propagators of Higher Order Abstract Cauchy Problems

In this paper, we present two quite general approximation theorems for the propagators of higher order (in time) abstract Cauchy problems, which extend largely the classical Trotter-Kato type approximation theorems for strongly continuous operator semigroups and cosine operator functions. Then, we apply the approximation theorems to deal with the second order dynamical boundary value problems.