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Entropy and Renormalized Solutions for the p(x)-Kaokacuab Equation with Measure Data
Variable exponents Entropy solutions Renormalized solutions Exist- ence Uniqueness
2015/5/4
In this paper we prove the existence and uniqueness of both entropy solutions and renormalized solutions for the p(x)-Laplacian equation with variable exponents and a signed measure in L 1 (Ω) +...
Existence of solutions and separation from singularities for a class of fourth order degenerate parabolic equations
degenerate fourth-order parabolic equation separation from singularities long-time behavior
2010/12/8
A nonlinear parabolic equation of the fourth order is analyzed. The equation is characterized
by a mobility coefficient that degenerates at 0. Existence of at least one weak solution is proved by usi...
Capacitary estimates of solutions of semilinear parabolic equations
Heat equation singularities Borel measures Bessel capacities Wiener type test
2010/12/13
We prove that any positive solution of ∂tu − u + uq = 0 (q > 1) in RN × (0,∞) with
initial trace (F, 0), where F is a closed subset of RN can be represented, up to two universal
multipl...
Entropy Solutions for a Non-Uniformly Parabolic Equation
Entropy solutions Existence Uniqueness Parabolic
2015/5/4
In this paper we prove the existence and uniqueness of entropy solutions for the initial-boundary value problem of a non-uniformly parabolic equation. Moreover, we establish a comparison result. Some ...
Renormalized and Entropy Solutions for Nonlinear Parabolic Equations with Variable Exponents and L1 Data
Variable exponents Renormalized solutions Entropy solutions Exist- ence Uniqueness
2015/5/4
Abstract. In this paper we prove the existence and uniqueness of both renormalized solutions and entropy solutions for nonlinear parabolic equations with variable exponents and L 1 data. And moreover,...
H¨older continuity of the weak solutions for parabolic equations with the nonstandard growth condition
Boundedness H\
2007/12/12
In this paper, we investigate the interior regularity including the local boundedness and the interior H\"{o}lder continuity of weak solutions for parabolic equations of the $p(x,t)$-Laplacian type. W...