On a class of forward -backward parabolic equations: Formation of singularities

被引:3
|
作者
Bertsch, M. [1 ,2 ]
Smarrazzo, F. [3 ]
Tesei, A. [2 ,4 ]
机构
[1] Univ Roma Tor Vergata, Dipartimento Matemat, Via Ric Sci, I-00133 Rome, Italy
[2] CNR, Ist Applicaz Calcolo M Picone, Rome, Italy
[3] Univ Campus Biomed Roma, Via A Portillo, Rome, Italy
[4] Sapienza Univ Roma, Dipartimento Matemat G Castelnuovo, Ple A Moro 5, I-00185 Rome, Italy
关键词
Forward-backward parabolic equations; Formation of singularities; Pseudo-parabolic regularization; Radon; measures; PSEUDOPARABOLIC REGULARIZATION; EXISTENCE; HEAT; MODEL;
D O I
10.1016/j.jde.2020.05.007
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We study the formation of singularities for the problem {u(t) = [phi(u)](xx) + epsilon[psi(u)](txx) in Omega x (0, T) phi(u) + epsilon[psi(u)](t) = 0 in partial derivative Omega x(0, T) u = u(0) >= 0 in Omega x {0}, where epsilon and Tare positive constants, Omega a bounded interval, u(0) a nonnegative Radon measure on Omega, phi a nonmonotone and nonnegative function with phi(0) = phi(infinity) = 0, and psi an increasing bounded function. We show that if u(0) is a bounded or continuous function, singularities may appear spontaneously. The class of singularities which can arise in finite time is remarkably large, and includes infinitely many Dirac masses and singular continuous measures. (c) 2020 Elsevier Inc. All rights reserved.
引用
收藏
页码:6656 / 6698
页数:43
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