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Existence and asymptotic behavior of Radon measure-valued solutions for a class of nonlinear parabolic equations
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DOI：10.1186/s13662-021-03668-3.png)
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Abstract
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In this paper we address the weak Radon measure-valued solutions associated with the Young measure for a class of nonlinear parabolic equations with initial data as a bounded Radon measure. This problem is described as follows: {u(t) = alpha mu(xx) + beta[phi(u)](xx) + f(u) in Q:= Omega x (0, T), u = 0 on partial derivative Omega x (0, T), u(X, 0) = u(0)(x) in Omega, where T > 0, Omega subset of R is a bounded interval, u0 is nonnegative bounded Radon measure on Omega, and a, beta >= 0, under suitable assumptions on phi and f. In this work we prove the existence and the decay estimate of suitably defined Radon measure-valued solutions for the problem mentioned above. In particular, we study the asymptotic behavior of these Radon measure-valued solutions.
Keywords:
Radon measure-valued solution
Nonlinear parabolic equations
Young measure
Asymptotic behavior
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