In this paper, we study a nonlinear hyperbolic-parabolic system modeling some biological phenomena. By semigroup theory and Leray-Schauder fixed point argument, the local existence and uniqueness of the weak solutions...In this paper, we study a nonlinear hyperbolic-parabolic system modeling some biological phenomena. By semigroup theory and Leray-Schauder fixed point argument, the local existence and uniqueness of the weak solutions for this system are proved. For the spatial dimension N = 1, the global existence of the weak solution will be established by the bootstrap argument.展开更多
The authors prove the local existence and uniqueness of weak solution of a hyperbolic-parabolic system and establish the global existence of the weak solution for this system for the spatial dimension n = 1.
We prove the local existence and uniqueness of week solution of the hyperbolic-parabolic Chemotaxis system with some nonlinear product terms. For one dimensional case, we prove also the global existence and uniqueness...We prove the local existence and uniqueness of week solution of the hyperbolic-parabolic Chemotaxis system with some nonlinear product terms. For one dimensional case, we prove also the global existence and uniqueness of the solution for the problem.展开更多
We investigate a model arising from biology, which is a hyperbolic- parabolic coupled system. First, we prove the global existence and asymptotic behavior of smooth solutions to the Cauchy problem without any smallnes...We investigate a model arising from biology, which is a hyperbolic- parabolic coupled system. First, we prove the global existence and asymptotic behavior of smooth solutions to the Cauchy problem without any smallness assumption on the initial data. Second, if the Hs ∩ Ll-norm of initial data is sufficiently small, we also establish decay rates of the global smooth solutions. In particular, the optimal L2 decay rate of the solution and the almost optimal L2 decay rate of the first-order derivatives of the solution are obtained. These results are obtained by constructing a new nonnegative convex entropy and combining spectral analysis with energy methods.展开更多
A global existence theorem is established for an initial-boundary value prob- lem, with time-dependent boundary data, arising in a lumped parameter model of pulse combustion; the model in question gives rise to a nonl...A global existence theorem is established for an initial-boundary value prob- lem, with time-dependent boundary data, arising in a lumped parameter model of pulse combustion; the model in question gives rise to a nonlinear mixed hyperbolic-parabolic sys- tem. Using results previously established for the associated linear problem, a fixed point argument is employed to prove local existence for a regularized version of the nonlinear problem with artificial viscosity. Appropriate a-priori estimates are then derived which imply that the local existence result can be extended to a global existence theorem for the regularized problem. Finally, a different set of a priori estimates is generated which allows for taking the limit as the artificial viscosity parameter converges to zero; the corresponding solution of the regularized problem is then proven to converge to the unique solution of the initial-boundary value problem for the original, nonlinear, hyperbolic-parabolic system.展开更多
In this paper,we discuss the-local existence of weak solutions for some hyperbolic parabolic systems modelling chemotaxis with memory term.The main methods we use are the fixed point theorem and semigroup theory.
This paper is concerned with the existence of global solutions to the Cauchy problem of a hyperbolic-parabolic coupled system with large initial data. To this end, we first construct its local solutions by the standar...This paper is concerned with the existence of global solutions to the Cauchy problem of a hyperbolic-parabolic coupled system with large initial data. To this end, we first construct its local solutions by the standard iteration technique, then we deduce the basic energy estimate by constructing a convex entropy-entropy flux pair to this system. Moreover, the L∞-estimates and H^2-estimates of solutions are obtained through some delicate estimates. In our results, we do not ask the far fields of the initial data to be equal and the initial data can be arbitrarily large which generalize the result obtained in [7].展开更多
The Cauchy problem of the non-isentropic Navier-Stokes-Poisson equations in multi-dimensions is considered. The global existence and pointwise estimates of the classical solution are given, which extend the optimal de...The Cauchy problem of the non-isentropic Navier-Stokes-Poisson equations in multi-dimensions is considered. The global existence and pointwise estimates of the classical solution are given, which extend the optimal decay rate in L^2-norm in [27] to the n n L^P（R^n） （P 〉 n/n-1）- norm.展开更多
In this paper we consider the initial boundary value problem of a hyperbolic-parabolic type system for image inpainting in a 2-D bounded domain, and establish the existence of weak solutions to the system by employing...In this paper we consider the initial boundary value problem of a hyperbolic-parabolic type system for image inpainting in a 2-D bounded domain, and establish the existence of weak solutions to the system by employing the method of vanishing viscosity.展开更多
文摘In this paper, we study a nonlinear hyperbolic-parabolic system modeling some biological phenomena. By semigroup theory and Leray-Schauder fixed point argument, the local existence and uniqueness of the weak solutions for this system are proved. For the spatial dimension N = 1, the global existence of the weak solution will be established by the bootstrap argument.
文摘The authors prove the local existence and uniqueness of weak solution of a hyperbolic-parabolic system and establish the global existence of the weak solution for this system for the spatial dimension n = 1.
文摘We prove the local existence and uniqueness of week solution of the hyperbolic-parabolic Chemotaxis system with some nonlinear product terms. For one dimensional case, we prove also the global existence and uniqueness of the solution for the problem.
文摘We investigate a model arising from biology, which is a hyperbolic- parabolic coupled system. First, we prove the global existence and asymptotic behavior of smooth solutions to the Cauchy problem without any smallness assumption on the initial data. Second, if the Hs ∩ Ll-norm of initial data is sufficiently small, we also establish decay rates of the global smooth solutions. In particular, the optimal L2 decay rate of the solution and the almost optimal L2 decay rate of the first-order derivatives of the solution are obtained. These results are obtained by constructing a new nonnegative convex entropy and combining spectral analysis with energy methods.
文摘A global existence theorem is established for an initial-boundary value prob- lem, with time-dependent boundary data, arising in a lumped parameter model of pulse combustion; the model in question gives rise to a nonlinear mixed hyperbolic-parabolic sys- tem. Using results previously established for the associated linear problem, a fixed point argument is employed to prove local existence for a regularized version of the nonlinear problem with artificial viscosity. Appropriate a-priori estimates are then derived which imply that the local existence result can be extended to a global existence theorem for the regularized problem. Finally, a different set of a priori estimates is generated which allows for taking the limit as the artificial viscosity parameter converges to zero; the corresponding solution of the regularized problem is then proven to converge to the unique solution of the initial-boundary value problem for the original, nonlinear, hyperbolic-parabolic system.
文摘In this paper,we discuss the-local existence of weak solutions for some hyperbolic parabolic systems modelling chemotaxis with memory term.The main methods we use are the fixed point theorem and semigroup theory.
基金Huijiang Zhao was supported by the National Natural Science Foundation of China (10871151)Changjiang Zhu was supported by the National Natural Science Foundation of China (10625105 and 10431060)the Program for New Century Excellent Talentsin University (NCET-04-0745)
文摘This paper is concerned with the existence of global solutions to the Cauchy problem of a hyperbolic-parabolic coupled system with large initial data. To this end, we first construct its local solutions by the standard iteration technique, then we deduce the basic energy estimate by constructing a convex entropy-entropy flux pair to this system. Moreover, the L∞-estimates and H^2-estimates of solutions are obtained through some delicate estimates. In our results, we do not ask the far fields of the initial data to be equal and the initial data can be arbitrarily large which generalize the result obtained in [7].
基金Z.G. Wu was supported by National Natural Science Foundation of China (11101112)W.K. Wang was supported by National Natural Science Foundation of China (11071162)
文摘The Cauchy problem of the non-isentropic Navier-Stokes-Poisson equations in multi-dimensions is considered. The global existence and pointwise estimates of the classical solution are given, which extend the optimal decay rate in L^2-norm in [27] to the n n L^P（R^n） （P 〉 n/n-1）- norm.
基金Supported by National Natural Science Foundation of China(Grant Nos.11101218,11071119)Natural Science Foundation for Colleges and Universities in Jiangsu Province of China(Grant No.11KJB110009)
文摘In this paper we consider the initial boundary value problem of a hyperbolic-parabolic type system for image inpainting in a 2-D bounded domain, and establish the existence of weak solutions to the system by employing the method of vanishing viscosity.
