Linear and Quasi-linear Equations of Parabolic Type

addition analogous arbitrary arguments assertions assume assumptions belongs boundary value problems bounded carried Cauchy problem Chapter Chapter II classical coefficients concerning connection consequently consider constant continuous converge corresponding cylinder defined definition denote depending derivatives determined differential distance domain easily elements equal to zero equation equation 1.1 established estimate example existence fact finite fixed formulate function function u(x given gives hence Holder holds identity indicated inequality initial integral introduce known lateral Lemma limit linear means method namely necessary norm obtain operator parabolic parameters positive possible potential present proof properties proved quantities relation remaining respect restrictions result right side satisfy smooth solution solvability space sufficiently Suppose surface Theorem Theorem 6.1 tion transform unique valid virtue vrai