stefan problems with nonlinear diffusion and convection abstract we consider a class of stefan type problems having a convection term and a pseudomonotone nonlinear diffusion operator assuming data in l 1 we prove existence uniqueness and stability in the framework of renormalized solutions existence is established from compactness and monotonicity arguments which yield stability of solutions with respect to l 1 convergence of the data uniqueness is proved through a classical l 1 contraction principle obtained by a refinement of the doubling variable technique which allows us to extend previous results to a more general class of nonlinear possibly degenerate operators

renormalised solutions of nonlinear parabolic problems with l1 data existence and uniqueness in this paper we prove the existence and uniqueness of a renormalised solution of the nonlinear problem where the data f and u 0 belong to l 1 0 t and l 1 and where the function a 0 t n n is monotone but not necessarily strictly monotone and defines a bounded coercive continuous operator from the space into its dual space the renormalised solution is an element of c 0 0 t l 1 such that its truncates t k u belong to with this solution satisfies the equation formally obtained by using in the equation the test function s u where belongs to and where s belongs to c with

renormalized solutions for nonlinear elliptic equations with variable exponents and l1 data abstract we prove existence and uniqueness of a renormalized solution to nonlinear elliptic equations with variable exponents and l 1 data the functional setting involves lebesgue sobolev space with variable exponents w 1 p

a pocket guide to nonlinear differential equations in musielak orlicz spaces abstract the musielak orlicz setting unifies variable exponent orlicz weighted sobolev and double phase spaces they inherit technical difficulties resulting from general growth and inhomogeneity in this survey we present an overview of developments of the theory of existence of pdes in the setting including reflexive and non reflexive cases as well as isotropic and anisotropic ones particular attention is paid to problems with data below natural duality in absence of lavrentiev s phenomenon

steady flow of non newtonian fluids monotonicity methods in generalized orlicz spaces abstract our purpose is to show the existence of weak solutions to steady flow of non newtonian incompressible fluids with nonstandard growth conditions of the cauchy stress tensor we are motivated by the fluids of strongly inhomogeneous behavior and characterized by rapid shear thickening since l p framework is not sufficient to capture the described model we describe the growth conditions with the help of a general x dependent convex function and formulate our problem in generalized orlicz spaces

well posedness of parabolic equations in the non reflexive and anisotropic musielak orlicz spaces in the class of renormalized solutions abstract we prove existence and uniqueness of renormalized solutions to general nonlinear parabolic equation in musielak orlicz space avoiding growth restrictions namely we consider t u div a x u f l 1 t on a lipschitz bounded domain in r n the growth of the weakly monotone vector field a is controlled by a generalized nonhomogeneous and anisotropic n function m the approach does not require any particular type of growth condition of m or its conjugate m neither 2 nor 2 the condition we impose on m is continuity of log holder type which results in good approximation properties of the space however the requirement of regularity can be skipped in the case of reflexive spaces the proof of the main results uses truncation ideas the young measures methods and monotonicity arguments uniqueness results from the comparison principle

existence and uniqueness of renormalized solutions to nonlinear elliptic equations with variable exponents and l1 data abstract we prove the existence and uniqueness of a renormalized solution to nonlinear elliptic equations with variable exponents and l 1 data the functional setting involves sobolev spaces with variable exponents w 1 p

semiflexible polymer in the half plane and statistics of the integral of a brownian curve a continuum model of a polymer with non zero bending energy fluctuating without overhangs in the half plane is considered the exact partition function is obtained from the marshall watson solution of the klein kramers equation for brownian motion in the half space the partition function contains information on probabilities associated with the integral of a brownian curve and reproduces sinai s t 5 4 result for the asymptotic first passage time density the t 5 2 dependence of a different passage probability implies a first order polymer adsorption transition for short range pinning potentials

renormalized solutions of nonlinear elliptic problems in generalized orlicz spaces abstract we study a general class of nonlinear elliptic problems associated with the differential inclusion x u div a x u f u f where f l 1 the vector field a is monotone in the second variable and satisfies a non standard growth condition described by an x dependent convex function that generalizes both l p x and classical orlicz settings using truncation techniques and a generalized minty method in the functional setting of non reflexive spaces we prove existence of renormalized solutions for general l 1 data under an additional strict monotonicity assumption uniqueness of the renormalized solution is established sufficient conditions are specified which guarantee that the renormalized solution is already a weak solution to the problem

existence of renormalized solutions to elliptic equation in musielak orlicz space abstract we prove existence of renormalized solutions to general nonlinear elliptic equation in musielak orlicz space avoiding growth restrictions namely we consider div a x u f l 1 on a lipschitz bounded domain in r n the growth of the monotone vector field a is controlled by a generalized nonhomogeneous and anisotropic n function m the approach does not require any particular type of growth condition of m or its conjugate m neither 2 nor 2 the condition we impose is log holder continuity of m which results in good approximation properties of the space the proof of the main results uses truncation ideas the young measures methods and monotonicity arguments

existence of renormalized solutions of degenerate elliptic parabolic problems we consider a general class of degenerate elliptic parabolic problems associated with the equation b t div a d f existence of renormalized solutions is established for general l 1 data uniqueness of renormalized solutions has already been shown in a previous work

persistence of a continuous stochastic process with discrete time sampling we introduce the concept of discrete time persistence which deals with zero crossings of a continuous stochastic process x t measured at discrete times t n delta t for a gaussian markov process with relaxation rate mu we show that the persistence no crossing probability decays as rho a n for large n where a exp mu delta t and we compute rho a to high precision we also define the concept of alternating persistence which corresponds to a 1 corresponding to motion in an unstable potential mu 0 there is a nonzero probability of having no zero crossings in infinite time and we show how to calculate it

persistence of non markovian gaussian stationary processes in discrete time the persistence of a stochastic variable is the probability that it does not cross a given level during a fixed time interval although persistence is a simple concept to understand it is in gener

an eigenvalue problem for the anisotropic φ laplacian abstract we study an eigenvalue problem involving a fully anisotropic elliptic differential operator in arbitrary orlicz sobolev spaces the relevant equations are associated with constrained minimization problems for integral functionals depending on the gradient of competing functions through general anisotropic n functions in particular the latter need neither be radial nor have a polynomial growth and are not even assumed to satisfy the so called 2 condition the resulting analysis requires the development of some new aspects of the theory of anisotropic orlicz sobolev spaces

variational inequalities in orlicz sobolev spaces on etudie l existence de solutions d inegalites variationnelles associees a des operateurs differentiels elliptiques

existence and uniqueness for a degenerate parabolic equation with l1 data in this paper we study existence and uniqueness of solutions for the boundary value problem with initial datum in l1 ut div a x du in 0 u a u on 0 u x 0 u0 x in where a is a caratheodory function satisfying the classical leray lions hypothesis a is the neumann boundary operator associated to a du the gradient of u and is a maximal monotone graph in r r with 0 0

nonequilibrium thermodynamics of feedback control we establish a general theory of feedback control on classical stochastic thermodynamic systems and generalize nonequilibrium equalities such as the fluctuation theorem and the jarzynski equality in the presence of feedback control with multiple measurements our results are generalizations of the previous relevant works to the situations with general measurements and multiple heat baths the obtained equalities involve additional terms that characterize the information obtained by measurements or the efficacy of feedback control a generalized szilard engine and a feedback controlled ratchet are shown to satisfy the derived equalities

renormalized solutions to nonlinear parabolic problems in generalized musielak orlicz spaces abstract we will present the proof of existence of renormalized solutions to a nonlinear parabolic problem t u div a d u f with right hand side f and initial data u 0 in l 1 the growth and coercivity conditions on the monotone vector field a are prescribed by a generalized n function m which is anisotropic and inhomogeneous with respect to the space variable in particular m does not have to satisfy an upper growth bound described by a 2 condition therefore we work with generalized musielak orlicz spaces which are not necessarily reflexive moreover we provide a weak sequential stability result for a more general problem t u div a d u f u f where is a monotone function with respect to the second variable and f is locally lipschitz continuous within the proof we use truncation methods young measure techniques the integration by parts formula and monotonicity arguments which have been adapted to nonreflexive musielak orlicz spaces

renormalized solutions for degenerate elliptic parabolic problems with nonlinear dynamical boundary conditions and l 1 data abstract we consider a degenerate elliptic parabolic problem with nonlinear dynamical boundary conditions assuming l 1 data we prove existence and uniqueness in the framework of renormalized solutions particular instances of this problem appear in various phenomena with changes of phase like multiphase stefan problems and in the weak formulation of the mathematical model of the so called hele shaw problem also the problem with non homogeneous neumann boundary condition is included

renormalized solutions for a nonlinear parabolic equation with variable exponents and l 1 data abstract we prove the well posedness existence and uniqueness of a renormalized solution to nonlinear parabolic equations with variable exponents and l 1 data the functional setting involves lebesgue sobolev spaces with variable exponents

structural stability for variable exponent elliptic problems i the p x laplacian kind problems abstract we study the structural stability i e the continuous dependence on coefficients of solutions of the elliptic problems under the form b u n div a n x u n f n the equation is set in a bounded domain of r n and supplied with the homogeneous dirichlet boundary condition on here b is a non decreasing function on r and a n x n is a family of applications which verifies the classical leray lions hypotheses but with a variable summability exponent p n x 1 p p n p the need for varying p x arises for instance in the numerical analysis of the p x laplacian problem uniqueness and existence for these problems are well understood by now we apply the stability properties to further generalize the existence results the continuous dependence result we prove is valid for weak and for renormalized solutions notice that besides being interesting on its own the renormalized solutions framework also permits us to deduce optimal convergence results for the weak solutions our technique avoids the use of a fixed duality framework like the w 0 1 p x w 1 p x duality and thus it is suitable for the study of problems where the summability exponent p also depends on the unknown solution itself in a local or in a non local way the sequel of this paper will be concerned with well posedness of some p u laplacian kind problems and with existence of solutions to elliptic systems with variable solution dependent growth exponent

uniqueness of renormalized solutions of degenerate elliptic parabolic problems we consider a general class of degenerate elliptic paraboic problems associated with the equation b v t div a v dv f using kruzhkov s method of doubling variables both in space and time we prove uniqueness and a comparison principle in l 1 for renormalized solutions

on the cauchy problem for boltzmann equations global existence and weak stability we study the large data cauchy problem for boltzmann equations with general collision kernels we prove that sequences of solutions which satisfy only the physically natural a priori bounds converge weakly in l to a solution from this stability result we deduce global existence of a solution to the cauchy problem our method relies upon recent compactness results for velocity averages a new formulation of the boltzmann equation which involves nonlinear normalization and an analysis of subsolutions and supersolutions it allows us to overcome the lack of strong a priori estimates and define a meaningful collision operator for general configurations

renormalized solutions to parabolic equations in time and space dependent anisotropic musielak orlicz spaces in absence of lavrentiev s phenomenon abstract the paper concerns existence and uniqueness of solutions to a nonlinear parabolic equation with merely integrable data on a lipschitz bounded domain in r n our focal point is to involve the leading nonlinear part of the operator whose growth is described by anisotropic n function m inhomogeneous in the space and the time variables the main goals are proven in absence of lavrentiev s phenomenon to ensure which we impose a certain type of balance of interplay between the behavior of m for large and small changes of time and space variables its instances are log holder continuity of variable exponent inhomogeneous in time and space or optimal closeness condition for powers in double phase spaces possibly changing in time new delicate approximation in time result is proven and applied in the construction of renormalized solutions

entropy solutions for a doubly nonlinear elliptic problem with variable exponent abstract we study the boundary value problem b u div a x u f in u 0 on where is a smooth bounded domain in r n n 3 and div a x u is a p x laplace type operator with p 1 a measurable function and b a continuous and nondecreasing function from r r we prove the existence and uniqueness of an entropy solution for l 1 data f