Nonlinear Well-Posedness and Rates of Decay in Thermoelasticitywith Second Sound
نویسندگان
چکیده
We consider the Cauchy problem in nonlinear thermoelasticity with second sound in one space dimension. Due to Cattaneo’s law, replacing Fourier’s law for heat conduction, the system is hyperbolic. We first investigate the local well-posedness as a strictly hyperbolic system, and then discuss the relation between energy estimates for non-symmetric hyperbolic systems and well-posedness. For the global small solution we describe the long time behavior and obtain decay rates of the L-norm.
منابع مشابه
COUPLED FIXED POINT THEOREMS FOR RATIONAL TYPE CONTRACTIONS VIA C-CLASS FUNCTIONS
In this paper, by using C-class functions, we will present a coupled xed problem in b-metric space for the single-valued operators satisfying a generalized contraction condition. First part of the paper is related to some xed point theorems, the second part presents the uniqueness and existence for the solution of the coupled xed point problem and in the third part we...
متن کاملCommon fixed points of four maps using generalized weak contractivity and well-posedness
In this paper, we introduce the concept of generalized -contractivityof a pair of maps w.r.t. another pair. We establish a common fixed point result fortwo pairs of self-mappings, when one of these pairs is generalized -contractionw.r.t. the other and study the well-posedness of their fixed point problem. Inparticular, our fixed point result extends the main result of a recent paper ofQingnian ...
متن کاملHadamard Well-posedness for a Family of Mixed Variational Inequalities and Inclusion Problems
In this paper, the concepts of well-posednesses and Hadamard well-posedness for a family of mixed variational inequalities are studied. Also, some metric characterizations of them are presented and some relations between well-posedness and Hadamard well-posedness of a family of mixed variational inequalities is studied. Finally, a relation between well-posedness for the family of mixed variatio...
متن کاملOn Nonlinear Nonlocal Diffusion Equations
This is a study of a class of nonlocal nonlinear diffusion equations (NNDEs). We present several new qualitative results for nonlocal Dirichlet problems. It is shown that solutions with positive initial data remain positive through time, even for nonlinear problems; in addition, we prove that solutions to these equations obey a strong maximum principle. A striking result shows that nonlocal sol...
متن کاملBlow up of positive initial-energy solutions for coupled nonlinear wave equations with degenerate damping and source terms
In [] Rammaha and Sakuntasathien studied the global well posedness of the solution of problem (.). Agre and Rammaha [] studied the global existence and the blow up of the solution of problem (.) for k = l = θ = = , and also Alves et al. [] investigated the existence, uniform decay rates and blow up of the solution to systems. After that, the blow up result was improved by Houari []. Al...
متن کامل